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= \\frac{1}{T} \\int_0^T 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ist der Mittelwert von ",[573,1758,1760,1773],{"className":1759},[576],[573,1761,1763],{"className":1762},[580],[582,1764,1765],{"xmlns":584},[586,1766,1767,1771],{},[589,1768,1769],{},[592,1770,1445],{},[616,1772,1445],{"encoding":618},[573,1774,1776],{"className":1775,"ariaHidden":624},[623],[573,1777,1779,1783],{"className":1778},[628],[573,1780],{"className":1781,"style":1782},[632],"height:0.8889em;vertical-align:-0.1944em;",[573,1784,1445],{"className":1785,"style":1737},[645,646],[891,1787,1788,1789,1817,1818,1912,1913,1941,1942,1181],{},"Ist ",[573,1790,1792,1805],{"className":1791},[576],[573,1793,1795],{"className":1794},[580],[582,1796,1797],{"xmlns":584},[586,1798,1799,1803],{},[589,1800,1801],{},[592,1802,1445],{},[616,1804,1445],{"encoding":618},[573,1806,1808],{"className":1807,"ariaHidden":624},[623],[573,1809,1811,1814],{"className":1810},[628],[573,1812],{"className":1813,"style":1782},[632],[573,1815,1445],{"className":1816,"style":1737},[645,646]," gerade, gilt 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f(x)^2\\,dx = \\frac{a_0^2}{2} + \\sum_{n=1}^{\\infty} \\left( a_n^2 + b_n^2 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x",[573,2732,2734,2761],{"className":2733,"ariaHidden":624},[623],[573,2735,2737,2740,2743,2746,2749,2752,2755,2758],{"className":2736},[628],[573,2738],{"className":2739,"style":633},[632],[573,2741,1445],{"className":2742,"style":1737},[645,646],[573,2744,602],{"className":2745},[641],[573,2747,611],{"className":2748},[645,646],[573,2750,614],{"className":2751},[655],[573,2753],{"className":2754,"style":1226},[949],[573,2756,1201],{"className":2757},[1230],[573,2759],{"className":2760,"style":1226},[949],[573,2762,2764,2767],{"className":2763},[628],[573,2765],{"className":2766,"style":1278},[632],[573,2768,611],{"className":2769},[645,646]," auf ",[573,2772,2774,2798],{"className":2773},[576],[573,2775,2777],{"className":2776},[580],[582,2778,2779],{"xmlns":584},[586,2780,2781,2795],{},[589,2782,2783,2785,2787,2789,2791,2793],{},[596,2784,602],{"stretchy":601},[596,2786,975],{},[592,2788,1206],{},[596,2790,917],{"separator":624},[592,2792,1206],{},[596,2794,614],{"stretchy":601},[616,2796,2797],{"encoding":618},"(-\\pi, \\pi)",[573,2799,2801],{"className":2800,"ariaHidden":624},[623],[573,2802,2804,2807,2810,2813,2816,2819,2822,2825],{"className":2803},[628],[573,2805],{"className":2806,"style":633},[632],[573,2808,602],{"className":2809},[641],[573,2811,975],{"className":2812},[645],[573,2814,1206],{"className":2815,"style":647},[645,646],[573,2817,917],{"className":2818},[945],[573,2820],{"className":2821,"style":950},[949],[573,2823,1206],{"className":2824,"style":647},[645,646],[573,2826,614],{"className":2827},[655],", 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Mit partieller Integration:",[573,3007,3009],{"className":3008},[2043],[573,3010,3012,3098],{"className":3011},[576],[573,3013,3015],{"className":3014},[580],[582,3016,3017],{"xmlns":584,"display":2052},[586,3018,3019,3095],{},[589,3020,3021,3027,3029,3035,3047,3049,3051,3053,3055,3057,3059,3061,3063,3065,3067,3069],{},[810,3022,3023,3025],{},[592,3024,1834],{},[592,3026,605],{},[596,3028,1201],{},[977,3030,3031,3033],{},[725,3032,1265],{},[592,3034,1206],{},[1434,3036,3037,3039,3045],{},[596,3038,1438],{},[589,3040,3041,3043],{},[596,3042,975],{},[592,3044,1206],{},[592,3046,1206],{},[592,3048,611],{},[592,3050,671],{},[596,3052,598],{},[596,3054,602],{"stretchy":601},[592,3056,605],{},[592,3058,611],{},[596,3060,614],{"stretchy":601},[1453,3062,1455],{},[592,3064,1458],{},[592,3066,611],{},[596,3068,1201],{},[977,3070,3071,3093],{},[589,3072,3073,3075,3077,3079,3081],{},[725,3074,983],{},[596,3076,602],{"stretchy":601},[596,3078,975],{},[725,3080,1265],{},[2078,3082,3083,3085],{},[596,3084,614],{"stretchy":601},[589,3086,3087,3089,3091],{},[592,3088,605],{},[596,3090,2106],{},[725,3092,1265],{},[592,3094,605],{},[616,3096,3097],{"encoding":618},"b_n = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} x \\sin(nx)\\,dx = \\frac{2(-1)^{n+1}}{n}",[573,3099,3101,3156,3332],{"className":3100,"ariaHidden":624},[623],[573,3102,3104,3107,3147,3150,3153],{"className":3103},[628],[573,3105],{"className":3106,"style":1853},[632],[573,3108,3110,3113],{"className":3109},[645],[573,3111,1834],{"className":3112},[645,646],[573,3114,3116],{"className":3115},[839],[573,3117,3119,3139],{"className":3118},[843,844],[573,3120,3122,3136],{"className":3121},[848],[573,3123,3125],{"className":3124,"style":853},[852],[573,3126,3127,3130],{"style":856},[573,3128],{"className":3129,"style":861},[860],[573,3131,3133],{"className":3132},[865,866,867,868],[573,3134,605],{"className":3135},[645,646,868],[573,3137,876],{"className":3138},[875],[573,3140,3142],{"className":3141},[848],[573,3143,3145],{"className":3144,"style":883},[852],[573,3146],{},[573,3148],{"className":3149,"style":1226},[949],[573,3151,1201],{"className":3152},[1230],[573,3154],{"className":3155,"style":1226},[949],[573,3157,3159,3163,3225,3228,3290,3293,3296,3299,3302,3305,3308,3311,3314,3317,3320,3323,3326,3329],{"className":3158},[628],[573,3160],{"className":3161,"style":3162},[632],"height:2.3846em;vertical-align:-0.9703em;",[573,3164,3166,3169,3222],{"className":3165},[645],[573,3167],{"className":3168},[641,1030],[573,3170,3172],{"className":3171},[977],[573,3173,3175,3214],{"className":3174},[843,844],[573,3176,3178,3211],{"className":3177},[848],[573,3179,3181,3192,3200],{"className":3180,"style":2180},[852],[573,3182,3183,3186],{"style":2183},[573,3184],{"className":3185,"style":1050},[860],[573,3187,3189],{"className":3188},[645],[573,3190,1206],{"className":3191,"style":647},[645,646],[573,3193,3194,3197],{"style":1062},[573,3195],{"className":3196,"style":1050},[860],[573,3198],{"className":3199,"style":1070},[1069],[573,3201,3202,3205],{"style":2203},[573,3203],{"className":3204,"style":1050},[860],[573,3206,3208],{"className":3207},[645],[573,3209,1265],{"className":3210},[645],[573,3212,876],{"className":3213},[875],[573,3215,3217],{"className":3216},[848],[573,3218,3220],{"className":3219,"style":2222},[852],[573,3221],{},[573,3223],{"className":3224},[655,1030],[573,3226],{"className":3227,"style":950},[949],[573,3229,3231,3234],{"className":3230},[637],[573,3232,1438],{"className":3233,"style":2238},[637,1679,2237],[573,3235,3237],{"className":3236},[839],[573,3238,3240,3281],{"className":3239},[843,844],[573,3241,3243,3278],{"className":3242},[848],[573,3244,3247,3264],{"className":3245,"style":3246},[852],"height:1.4143em;",[573,3248,3249,3252],{"style":2254},[573,3250],{"className":3251,"style":861},[860],[573,3253,3255],{"className":3254},[865,866,867,868],[573,3256,3258,3261],{"className":3257},[645,868],[573,3259,975],{"className":3260},[645,868],[573,3262,1206],{"className":3263,"style":647},[645,646,868],[573,3265,3266,3269],{"style":2266},[573,3267],{"className":3268,"style":861},[860],[573,3270,3272],{"className":3271},[865,866,867,868],[573,3273,3275],{"className":3274},[645,868],[573,3276,1206],{"className":3277,"style":647},[645,646,868],[573,3279,876],{"className":3280},[875],[573,3282,3284],{"className":3283},[848],[573,3285,3288],{"className":3286,"style":3287},[852],"height:0.9703em;",[573,3289],{},[573,3291],{"className":3292,"style":950},[949],[573,3294,611],{"className":3295},[645,646],[573,3297],{"className":3298,"style":950},[949],[573,3300,671],{"className":3301},[637],[573,3303,602],{"className":3304},[641],[573,3306,605],{"className":3307},[645,646],[573,3309,611],{"className":3310},[645,646],[573,3312,614],{"className":3313},[655],[573,3315],{"className":3316,"style":950},[949],[573,3318,1458],{"className":3319},[645,646],[573,3321,611],{"className":3322},[645,646],[573,3324],{"className":3325,"style":1226},[949],[573,3327,1201],{"className":3328},[1230],[573,3330],{"className":3331,"style":1226},[949],[573,3333,3335,3338],{"className":3334},[628],[573,3336],{"className":3337,"style":2355},[632],[573,3339,3341,3344,3444],{"className":3340},[645],[573,3342],{"className":3343},[641,1030],[573,3345,3347],{"className":3346},[977],[573,3348,3350,3436],{"className":3349},[843,844],[573,3351,3353,3433],{"className":3352},[848],[573,3354,3356,3367,3375],{"className":3355,"style":2374},[852],[573,3357,3358,3361],{"style":2183},[573,3359],{"className":3360,"style":1050},[860],[573,3362,3364],{"className":3363},[645],[573,3365,605],{"className":3366},[645,646],[573,3368,3369,3372],{"style":1062},[573,3370],{"className":3371,"style":1050},[860],[573,3373],{"className":3374,"style":1070},[1069],[573,3376,3377,3380],{"style":2203},[573,3378],{"className":3379,"style":1050},[860],[573,3381,3383,3386,3389,3392,3395],{"className":3382},[645],[573,3384,983],{"className":3385},[645],[573,3387,602],{"className":3388},[641],[573,3390,975],{"className":3391},[645],[573,3393,1265],{"className":3394},[645],[573,3396,3398,3401],{"className":3397},[655],[573,3399,614],{"className":3400},[655],[573,3402,3404],{"className":3403},[839],[573,3405,3407],{"className":3406},[843],[573,3408,3410],{"className":3409},[848],[573,3411,3413],{"className":3412,"style":2420},[852],[573,3414,3415,3418],{"style":2435},[573,3416],{"className":3417,"style":861},[860],[573,3419,3421],{"className":3420},[865,866,867,868],[573,3422,3424,3427,3430],{"className":3423},[645,868],[573,3425,605],{"className":3426},[645,646,868],[573,3428,2106],{"className":3429},[2478,868],[573,3431,1265],{"className":3432},[645,868],[573,3434,876],{"className":3435},[875],[573,3437,3439],{"className":3438},[848],[573,3440,3442],{"className":3441,"style":2222},[852],[573,3443],{},[573,3445],{"className":3446},[655,1030],[564,3448,3449,3450,2828,3543,2828,3641,3803,3804,4298,4299,1181],{},"Also ",[573,3451,3453,3475],{"className":3452},[576],[573,3454,3456],{"className":3455},[580],[582,3457,3458],{"xmlns":584},[586,3459,3460,3472],{},[589,3461,3462,3468,3470],{},[810,3463,3464,3466],{},[592,3465,1834],{},[725,3467,1265],{},[596,3469,1201],{},[725,3471,983],{},[616,3473,3474],{"encoding":618},"b_1 = 2",[573,3476,3478,3534],{"className":3477,"ariaHidden":624},[623],[573,3479,3481,3484,3525,3528,3531],{"className":3480},[628],[573,3482],{"className":3483,"style":1853},[632],[573,3485,3487,3490],{"className":3486},[645],[573,3488,1834],{"className":3489},[645,646],[573,3491,3493],{"className":3492},[839],[573,3494,3496,3517],{"className":3495},[843,844],[573,3497,3499,3514],{"className":3498},[848],[573,3500,3503],{"className":3501,"style":3502},[852],"height:0.3011em;",[573,3504,3505,3508],{"style":856},[573,3506],{"className":3507,"style":861},[860],[573,3509,3511],{"className":3510},[865,866,867,868],[573,3512,1265],{"className":3513},[645,868],[573,3515,876],{"className":3516},[875],[573,3518,3520],{"className":3519},[848],[573,3521,3523],{"className":3522,"style":883},[852],[573,3524],{},[573,3526],{"className":3527,"style":1226},[949],[573,3529,1201],{"className":3530},[1230],[573,3532],{"className":3533,"style":1226},[949],[573,3535,3537,3540],{"className":3536},[628],[573,3538],{"className":3539,"style":739},[632],[573,3541,983],{"className":3542},[645],[573,3544,3546,3570],{"className":3545},[576],[573,3547,3549],{"className":3548},[580],[582,3550,3551],{"xmlns":584},[586,3552,3553,3567],{},[589,3554,3555,3561,3563,3565],{},[810,3556,3557,3559],{},[592,3558,1834],{},[725,3560,983],{},[596,3562,1201],{},[596,3564,975],{},[725,3566,1265],{},[616,3568,3569],{"encoding":618},"b_2 = -1",[573,3571,3573,3628],{"className":3572,"ariaHidden":624},[623],[573,3574,3576,3579,3619,3622,3625],{"className":3575},[628],[573,3577],{"className":3578,"style":1853},[632],[573,3580,3582,3585],{"className":3581},[645],[573,3583,1834],{"className":3584},[645,646],[573,3586,3588],{"className":3587},[839],[573,3589,3591,3611],{"className":3590},[843,844],[573,3592,3594,3608],{"className":3593},[848],[573,3595,3597],{"className":3596,"style":3502},[852],[573,3598,3599,3602],{"style":856},[573,3600],{"className":3601,"style":861},[860],[573,3603,3605],{"className":3604},[865,866,867,868],[573,3606,983],{"className":3607},[645,868],[573,3609,876],{"className":3610},[875],[573,3612,3614],{"className":3613},[848],[573,3615,3617],{"className":3616,"style":883},[852],[573,3618],{},[573,3620],{"className":3621,"style":1226},[949],[573,3623,1201],{"className":3624},[1230],[573,3626],{"className":3627,"style":1226},[949],[573,3629,3631,3635,3638],{"className":3630},[628],[573,3632],{"className":3633,"style":3634},[632],"height:0.7278em;vertical-align:-0.0833em;",[573,3636,975],{"className":3637},[645],[573,3639,1265],{"className":3640},[645],[573,3642,3644,3671],{"className":3643},[576],[573,3645,3647],{"className":3646},[580],[582,3648,3649],{"xmlns":584},[586,3650,3651,3668],{},[589,3652,3653,3660,3662],{},[810,3654,3655,3657],{},[592,3656,1834],{},[725,3658,3659],{},"3",[596,3661,1201],{},[977,3663,3664,3666],{},[725,3665,983],{},[725,3667,3659],{},[616,3669,3670],{"encoding":618},"b_3 = \\frac{2}{3}",[573,3672,3674,3729],{"className":3673,"ariaHidden":624},[623],[573,3675,3677,3680,3720,3723,3726],{"className":3676},[628],[573,3678],{"className":3679,"style":1853},[632],[573,3681,3683,3686],{"className":3682},[645],[573,3684,1834],{"className":3685},[645,646],[573,3687,3689],{"className":3688},[839],[573,3690,3692,3712],{"className":3691},[843,844],[573,3693,3695,3709],{"className":3694},[848],[573,3696,3698],{"className":3697,"style":3502},[852],[573,3699,3700,3703],{"style":856},[573,3701],{"className":3702,"style":861},[860],[573,3704,3706],{"className":3705},[865,866,867,868],[573,3707,3659],{"className":3708},[645,868],[573,3710,876],{"className":3711},[875],[573,3713,3715],{"className":3714},[848],[573,3716,3718],{"className":3717,"style":883},[852],[573,3719],{},[573,3721],{"className":3722,"style":1226},[949],[573,3724,1201],{"className":3725},[1230],[573,3727],{"className":3728,"style":1226},[949],[573,3730,3732,3735],{"className":3731},[628],[573,3733],{"className":3734,"style":1331},[632],[573,3736,3738,3741,3800],{"className":3737},[645],[573,3739],{"className":3740},[641,1030],[573,3742,3744],{"className":3743},[977],[573,3745,3747,3792],{"className":3746},[843,844],[573,3748,3750,3789],{"className":3749},[848],[573,3751,3753,3767,3775],{"className":3752,"style":1350},[852],[573,3754,3755,3758],{"style":1046},[573,3756],{"className":3757,"style":1050},[860],[573,3759,3761],{"className":3760},[865,866,867,868],[573,3762,3764],{"className":3763},[645,868],[573,3765,3659],{"className":3766},[645,868],[573,3768,3769,3772],{"style":1062},[573,3770],{"className":3771,"style":1050},[860],[573,3773],{"className":3774,"style":1070},[1069],[573,3776,3777,3780],{"style":1073},[573,3778],{"className":3779,"style":1050},[860],[573,3781,3783],{"className":3782},[865,866,867,868],[573,3784,3786],{"className":3785},[645,868],[573,3787,983],{"className":3788},[645,868],[573,3790,876],{"className":3791},[875],[573,3793,3795],{"className":3794},[848],[573,3796,3798],{"className":3797,"style":1095},[852],[573,3799],{},[573,3801],{"className":3802},[655,1030],". Mit Parseval folgt ",[573,3805,3807,3880],{"className":3806},[576],[573,3808,3810],{"className":3809},[580],[582,3811,3812],{"xmlns":584},[586,3813,3814,3877],{},[589,3815,3816,3822,3834,3840,3842,3844,3846,3848,3862,3864,3866],{},[977,3817,3818,3820],{},[725,3819,1265],{},[592,3821,1206],{},[1434,3823,3824,3826,3832],{},[596,3825,1438],{},[589,3827,3828,3830],{},[596,3829,975],{},[592,3831,1206],{},[592,3833,1206],{},[2078,3835,3836,3838],{},[592,3837,611],{},[725,3839,983],{},[1453,3841,1455],{},[592,3843,1458],{},[592,3845,611],{},[596,3847,1201],{},[977,3849,3850,3860],{},[589,3851,3852,3854],{},[725,3853,983],{},[2078,3855,3856,3858],{},[592,3857,1206],{},[725,3859,983],{},[725,3861,3659],{},[596,3863,1201],{},[596,3865,2112],{},[977,3867,3868,3871],{},[725,3869,3870],{},"4",[2078,3872,3873,3875],{},[592,3874,605],{},[725,3876,983],{},[616,3878,3879],{"encoding":618},"\\frac{1}{\\pi}\\int_{-\\pi}^{\\pi} x^2\\,dx = \\frac{2\\pi^2}{3} = \\sum \\frac{4}{n^2}",[573,3881,3883,4073,4189],{"className":3882,"ariaHidden":624},[623],[573,3884,3886,3890,3958,3961,4023,4026,4055,4058,4061,4064,4067,4070],{"className":3885},[628],[573,3887],{"className":3888,"style":3889},[632],"height:1.2734em;vertical-align:-0.4142em;",[573,3891,3893,3896,3955],{"className":3892},[645],[573,3894],{"className":3895},[641,1030],[573,3897,3899],{"className":3898},[977],[573,3900,3902,3947],{"className":3901},[843,844],[573,3903,3905,3944],{"className":3904},[848],[573,3906,3908,3922,3930],{"className":3907,"style":1350},[852],[573,3909,3910,3913],{"style":1046},[573,3911],{"className":3912,"style":1050},[860],[573,3914,3916],{"className":3915},[865,866,867,868],[573,3917,3919],{"className":3918},[645,868],[573,3920,1206],{"className":3921,"style":647},[645,646,868],[573,3923,3924,3927],{"style":1062},[573,3925],{"className":3926,"style":1050},[860],[573,3928],{"className":3929,"style":1070},[1069],[573,3931,3932,3935],{"style":1073},[573,3933],{"className":3934,"style":1050},[860],[573,3936,3938],{"className":3937},[865,866,867,868],[573,3939,3941],{"className":3940},[645,868],[573,3942,1265],{"className":3943},[645,868],[573,3945,876],{"className":3946},[875],[573,3948,3950],{"className":3949},[848],[573,3951,3953],{"className":3952,"style":1095},[852],[573,3954],{},[573,3956],{"className":3957},[655,1030],[573,3959],{"className":3960,"style":950},[949],[573,3962,3964,3967],{"className":3963},[637],[573,3965,1438],{"className":3966,"style":1681},[637,1679,1680],[573,3968,3970],{"className":3969},[839],[573,3971,3973,4014],{"className":3972},[843,844],[573,3974,3976,4011],{"className":3975},[848],[573,3977,3980,3997],{"className":3978,"style":3979},[852],"height:0.8593em;",[573,3981,3982,3985],{"style":1697},[573,3983],{"className":3984,"style":861},[860],[573,3986,3988],{"className":3987},[865,866,867,868],[573,3989,3991,3994],{"className":3990},[645,868],[573,3992,975],{"className":3993},[645,868],[573,3995,1206],{"className":3996,"style":647},[645,646,868],[573,3998,3999,4002],{"style":1709},[573,4000],{"className":4001,"style":861},[860],[573,4003,4005],{"className":4004},[865,866,867,868],[573,4006,4008],{"className":4007},[645,868],[573,4009,1206],{"className":4010,"style":647},[645,646,868],[573,4012,876],{"className":4013},[875],[573,4015,4017],{"className":4016},[848],[573,4018,4021],{"className":4019,"style":4020},[852],"height:0.4142em;",[573,4022],{},[573,4024],{"className":4025,"style":950},[949],[573,4027,4029,4032],{"className":4028},[645],[573,4030,611],{"className":4031},[645,646],[573,4033,4035],{"className":4034},[839],[573,4036,4038],{"className":4037},[843],[573,4039,4041],{"className":4040},[848],[573,4042,4044],{"className":4043,"style":2420},[852],[573,4045,4046,4049],{"style":2435},[573,4047],{"className":4048,"style":861},[860],[573,4050,4052],{"className":4051},[865,866,867,868],[573,4053,983],{"className":4054},[645,868],[573,4056],{"className":4057,"style":950},[949],[573,4059,1458],{"className":4060},[645,646],[573,4062,611],{"className":4063},[645,646],[573,4065],{"className":4066,"style":1226},[949],[573,4068,1201],{"className":4069},[1230],[573,4071],{"className":4072,"style":1226},[949],[573,4074,4076,4080,4180,4183,4186],{"className":4075},[628],[573,4077],{"className":4078,"style":4079},[632],"height:1.3629em;vertical-align:-0.345em;",[573,4081,4083,4086,4177],{"className":4082},[645],[573,4084],{"className":4085},[641,1030],[573,4087,4089],{"className":4088},[977],[573,4090,4092,4169],{"className":4091},[843,844],[573,4093,4095,4166],{"className":4094},[848],[573,4096,4099,4113,4121],{"className":4097,"style":4098},[852],"height:1.0179em;",[573,4100,4101,4104],{"style":1046},[573,4102],{"className":4103,"style":1050},[860],[573,4105,4107],{"className":4106},[865,866,867,868],[573,4108,4110],{"className":4109},[645,868],[573,4111,3659],{"className":4112},[645,868],[573,4114,4115,4118],{"style":1062},[573,4116],{"className":4117,"style":1050},[860],[573,4119],{"className":4120,"style":1070},[1069],[573,4122,4123,4126],{"style":1073},[573,4124],{"className":4125,"style":1050},[860],[573,4127,4129],{"className":4128},[865,866,867,868],[573,4130,4132,4135],{"className":4131},[645,868],[573,4133,983],{"className":4134},[645,868],[573,4136,4138,4141],{"className":4137},[645,868],[573,4139,1206],{"className":4140,"style":647},[645,646,868],[573,4142,4144],{"className":4143},[839],[573,4145,4147],{"className":4146},[843],[573,4148,4150],{"className":4149},[848],[573,4151,4154],{"className":4152,"style":4153},[852],"height:0.8913em;",[573,4155,4157,4160],{"style":4156},"top:-2.931em;margin-right:0.0714em;",[573,4158],{"className":4159,"style":1552},[860],[573,4161,4163],{"className":4162},[865,1556,1020,868],[573,4164,983],{"className":4165},[645,868],[573,4167,876],{"className":4168},[875],[573,4170,4172],{"className":4171},[848],[573,4173,4175],{"className":4174,"style":1095},[852],[573,4176],{},[573,4178],{"className":4179},[655,1030],[573,4181],{"className":4182,"style":1226},[949],[573,4184,1201],{"className":4185},[1230],[573,4187],{"className":4188,"style":1226},[949],[573,4190,4192,4195,4199,4202],{"className":4191},[628],[573,4193],{"className":4194,"style":1331},[632],[573,4196,2112],{"className":4197,"style":4198},[637,1679,1680],"position:relative;top:0em;",[573,4200],{"className":4201,"style":950},[949],[573,4203,4205,4208,4295],{"className":4204},[645],[573,4206],{"className":4207},[641,1030],[573,4209,4211],{"className":4210},[977],[573,4212,4214,4287],{"className":4213},[843,844],[573,4215,4217,4284],{"className":4216},[848],[573,4218,4220,4262,4270],{"className":4219,"style":1350},[852],[573,4221,4222,4225],{"style":1046},[573,4223],{"className":4224,"style":1050},[860],[573,4226,4228],{"className":4227},[865,866,867,868],[573,4229,4231],{"className":4230},[645,868],[573,4232,4234,4237],{"className":4233},[645,868],[573,4235,605],{"className":4236},[645,646,868],[573,4238,4240],{"className":4239},[839],[573,4241,4243],{"className":4242},[843],[573,4244,4246],{"className":4245},[848],[573,4247,4250],{"className":4248,"style":4249},[852],"height:0.7463em;",[573,4251,4253,4256],{"style":4252},"top:-2.786em;margin-right:0.0714em;",[573,4254],{"className":4255,"style":1552},[860],[573,4257,4259],{"className":4258},[865,1556,1020,868],[573,4260,983],{"className":4261},[645,868],[573,4263,4264,4267],{"style":1062},[573,4265],{"className":4266,"style":1050},[860],[573,4268],{"className":4269,"style":1070},[1069],[573,4271,4272,4275],{"style":1073},[573,4273],{"className":4274,"style":1050},[860],[573,4276,4278],{"className":4277},[865,866,867,868],[573,4279,4281],{"className":4280},[645,868],[573,4282,3870],{"className":4283},[645,868],[573,4285,876],{"className":4286},[875],[573,4288,4290],{"className":4289},[848],[573,4291,4293],{"className":4292,"style":1095},[852],[573,4294],{},[573,4296],{"className":4297},[655,1030],", also ",[573,4300,4302,4339],{"className":4301},[576],[573,4303,4305],{"className":4304},[580],[582,4306,4307],{"xmlns":584},[586,4308,4309,4336],{},[589,4310,4311,4313,4323,4325],{},[596,4312,2112],{},[977,4314,4315,4317],{},[725,4316,1265],{},[2078,4318,4319,4321],{},[592,4320,605],{},[725,4322,983],{},[596,4324,1201],{},[977,4326,4327,4333],{},[2078,4328,4329,4331],{},[592,4330,1206],{},[725,4332,983],{},[725,4334,4335],{},"6",[616,4337,4338],{"encoding":618},"\\sum \\frac{1}{n^2} = \\frac{\\pi^2}{6}",[573,4340,4342,4457],{"className":4341,"ariaHidden":624},[623],[573,4343,4345,4348,4351,4354,4448,4451,4454],{"className":4344},[628],[573,4346],{"className":4347,"style":1331},[632],[573,4349,2112],{"className":4350,"style":4198},[637,1679,1680],[573,4352],{"className":4353,"style":950},[949],[573,4355,4357,4360,4445],{"className":4356},[645],[573,4358],{"className":4359},[641,1030],[573,4361,4363],{"className":4362},[977],[573,4364,4366,4437],{"className":4365},[843,844],[573,4367,4369,4434],{"className":4368},[848],[573,4370,4372,4412,4420],{"className":4371,"style":1350},[852],[573,4373,4374,4377],{"style":1046},[573,4375],{"className":4376,"style":1050},[860],[573,4378,4380],{"className":4379},[865,866,867,868],[573,4381,4383],{"className":4382},[645,868],[573,4384,4386,4389],{"className":4385},[645,868],[573,4387,605],{"className":4388},[645,646,868],[573,4390,4392],{"className":4391},[839],[573,4393,4395],{"className":4394},[843],[573,4396,4398],{"className":4397},[848],[573,4399,4401],{"className":4400,"style":4249},[852],[573,4402,4403,4406],{"style":4252},[573,4404],{"className":4405,"style":1552},[860],[573,4407,4409],{"className":4408},[865,1556,1020,868],[573,4410,983],{"className":4411},[645,868],[573,4413,4414,4417],{"style":1062},[573,4415],{"className":4416,"style":1050},[860],[573,4418],{"className":4419,"style":1070},[1069],[573,4421,4422,4425],{"style":1073},[573,4423],{"className":4424,"style":1050},[860],[573,4426,4428],{"className":4427},[865,866,867,868],[573,4429,4431],{"className":4430},[645,868],[573,4432,1265],{"className":4433},[645,868],[573,4435,876],{"className":4436},[875],[573,4438,4440],{"className":4439},[848],[573,4441,4443],{"className":4442,"style":1095},[852],[573,4444],{},[573,4446],{"className":4447},[655,1030],[573,4449],{"className":4450,"style":1226},[949],[573,4452,1201],{"className":4453},[1230],[573,4455],{"className":4456,"style":1226},[949],[573,4458,4460,4463],{"className":4459},[628],[573,4461],{"className":4462,"style":4079},[632],[573,4464,4466,4469,4554],{"className":4465},[645],[573,4467],{"className":4468},[641,1030],[573,4470,4472],{"className":4471},[977],[573,4473,4475,4546],{"className":4474},[843,844],[573,4476,4478,4543],{"className":4477},[848],[573,4479,4481,4495,4503],{"className":4480,"style":4098},[852],[573,4482,4483,4486],{"style":1046},[573,4484],{"className":4485,"style":1050},[860],[573,4487,4489],{"className":4488},[865,866,867,868],[573,4490,4492],{"className":4491},[645,868],[573,4493,4335],{"className":4494},[645,868],[573,4496,4497,4500],{"style":1062},[573,4498],{"className":4499,"style":1050},[860],[573,4501],{"className":4502,"style":1070},[1069],[573,4504,4505,4508],{"style":1073},[573,4506],{"className":4507,"style":1050},[860],[573,4509,4511],{"className":4510},[865,866,867,868],[573,4512,4514],{"className":4513},[645,868],[573,4515,4517,4520],{"className":4516},[645,868],[573,4518,1206],{"className":4519,"style":647},[645,646,868],[573,4521,4523],{"className":4522},[839],[573,4524,4526],{"className":4525},[843],[573,4527,4529],{"className":4528},[848],[573,4530,4532],{"className":4531,"style":4153},[852],[573,4533,4534,4537],{"style":4156},[573,4535],{"className":4536,"style":1552},[860],[573,4538,4540],{"className":4539},[865,1556,1020,868],[573,4541,983],{"className":4542},[645,868],[573,4544,876],{"className":4545},[875],[573,4547,4549],{"className":4548},[848],[573,4550,4552],{"className":4551,"style":1095},[852],[573,4553],{},[573,4555],{"className":4556},[655,1030],[564,4558,4559,2703,4562,2770,4639,2884,4695,4723,4724,4815,4816,5107],{},[568,4560,4561],{},"Dreieckschwingung",[573,4563,4565,4594],{"className":4564},[576],[573,4566,4568],{"className":4567},[580],[582,4569,4570],{"xmlns":584},[586,4571,4572,4591],{},[589,4573,4574,4576,4578,4580,4582,4584,4587,4589],{},[592,4575,1445],{},[596,4577,602],{"stretchy":601},[592,4579,611],{},[596,4581,614],{"stretchy":601},[596,4583,1201],{},[592,4585,4586],{"mathvariant":2123},"∣",[592,4588,611],{},[592,4590,4586],{"mathvariant":2123},[616,4592,4593],{"encoding":618},"f(x) = |x|",[573,4595,4597,4624],{"className":4596,"ariaHidden":624},[623],[573,4598,4600,4603,4606,4609,4612,4615,4618,4621],{"className":4599},[628],[573,4601],{"className":4602,"style":633},[632],[573,4604,1445],{"className":4605,"style":1737},[645,646],[573,4607,602],{"className":4608},[641],[573,4610,611],{"className":4611},[645,646],[573,4613,614],{"className":4614},[655],[573,4616],{"className":4617,"style":1226},[949],[573,4619,1201],{"className":4620},[1230],[573,4622],{"className":4623,"style":1226},[949],[573,4625,4627,4630,4633,4636],{"className":4626},[628],[573,4628],{"className":4629,"style":633},[632],[573,4631,4586],{"className":4632},[645],[573,4634,611],{"className":4635},[645,646],[573,4637,4586],{"className":4638},[645],[573,4640,4642,4665],{"className":4641},[576],[573,4643,4645],{"className":4644},[580],[582,4646,4647],{"xmlns":584},[586,4648,4649,4663],{},[589,4650,4651,4653,4655,4657,4659,4661],{},[596,4652,602],{"stretchy":601},[596,4654,975],{},[592,4656,1206],{},[596,4658,917],{"separator":624},[592,4660,1206],{},[596,4662,614],{"stretchy":601},[616,4664,2797],{"encoding":618},[573,4666,4668],{"className":4667,"ariaHidden":624},[623],[573,4669,4671,4674,4677,4680,4683,4686,4689,4692],{"className":4670},[628],[573,4672],{"className":4673,"style":633},[632],[573,4675,602],{"className":4676},[641],[573,4678,975],{"className":4679},[645],[573,4681,1206],{"className":4682,"style":647},[645,646],[573,4684,917],{"className":4685},[945],[573,4687],{"className":4688,"style":950},[949],[573,4690,1206],{"className":4691,"style":647},[645,646],[573,4693,614],{"className":4694},[655],[573,4696,4698,4711],{"className":4697},[576],[573,4699,4701],{"className":4700},[580],[582,4702,4703],{"xmlns":584},[586,4704,4705,4709],{},[589,4706,4707],{},[592,4708,1445],{},[616,4710,1445],{"encoding":618},[573,4712,4714],{"className":4713,"ariaHidden":624},[623],[573,4715,4717,4720],{"className":4716},[628],[573,4718],{"className":4719,"style":1782},[632],[573,4721,1445],{"className":4722,"style":1737},[645,646]," ist gerade, also 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Es ist ",[573,4817,4819,4873],{"className":4818},[576],[573,4820,4822],{"className":4821},[580],[582,4823,4824],{"xmlns":584},[586,4825,4826,4870],{},[589,4827,4828,4834,4836,4842,4854,4856,4858,4860,4862,4864,4866,4868],{},[810,4829,4830,4832],{},[592,4831,814],{},[725,4833,727],{},[596,4835,1201],{},[977,4837,4838,4840],{},[725,4839,1265],{},[592,4841,1206],{},[1434,4843,4844,4846,4852],{},[596,4845,1438],{},[589,4847,4848,4850],{},[596,4849,975],{},[592,4851,1206],{},[592,4853,1206],{},[592,4855,4586],{"mathvariant":2123},[592,4857,611],{},[592,4859,4586],{"mathvariant":2123},[1453,4861,1455],{},[592,4863,1458],{},[592,4865,611],{},[596,4867,1201],{},[592,4869,1206],{},[616,4871,4872],{"encoding":618},"a_0 = \\frac{1}{\\pi}\\int_{-\\pi}^{\\pi} |x|\\,dx = 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und",[573,5109,5111],{"className":5110},[2043],[573,5112,5114,5171],{"className":5113},[576],[573,5115,5117],{"className":5116},[580],[582,5118,5119],{"xmlns":584,"display":2052},[586,5120,5121,5168],{},[589,5122,5123,5129,5131],{},[810,5124,5125,5127],{},[592,5126,814],{},[592,5128,605],{},[596,5130,1201],{},[977,5132,5133,5158],{},[589,5134,5135,5137,5140,5142,5144,5146,5152,5154,5156],{},[725,5136,983],{},[596,5138,602],{"fence":624,"stretchy":624,"minsize":5139,"maxsize":5139},"1.2em",[596,5141,602],{"stretchy":601},[596,5143,975],{},[725,5145,1265],{},[2078,5147,5148,5150],{},[596,5149,614],{"stretchy":601},[592,5151,605],{},[596,5153,975],{},[725,5155,1265],{},[596,5157,614],{"fence":624,"stretchy":624,"minsize":5139,"maxsize":5139},[589,5159,5160,5162],{},[592,5161,1206],{},[2078,5163,5164,5166],{},[592,5165,605],{},[725,5167,983],{},[616,5169,5170],{"encoding":618},"a_n = \\frac{2\\bigl((-1)^n - 1\\bigr)}{\\pi 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gerade 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für ungerade ",[573,5518,5520,5533],{"className":5519},[576],[573,5521,5523],{"className":5522},[580],[582,5524,5525],{"xmlns":584},[586,5526,5527,5531],{},[589,5528,5529],{},[592,5530,605],{},[616,5532,605],{"encoding":618},[573,5534,5536],{"className":5535,"ariaHidden":624},[623],[573,5537,5539,5542],{"className":5538},[628],[573,5540],{"className":5541,"style":1278},[632],[573,5543,605],{"className":5544},[645,646],[573,5546,5548,5584],{"className":5547},[576],[573,5549,5551],{"className":5550},[580],[582,5552,5553],{"xmlns":584},[586,5554,5555,5581],{},[589,5556,5557,5563,5565,5567],{},[810,5558,5559,5561],{},[592,5560,814],{},[592,5562,605],{},[596,5564,1201],{},[596,5566,975],{},[977,5568,5569,5571],{},[725,5570,3870],{},[589,5572,5573,5575],{},[592,5574,1206],{},[2078,5576,5577,5579],{},[592,5578,605],{},[725,5580,983],{},[616,5582,5583],{"encoding":618},"a_n = -\\frac{4}{\\pi 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= -\\frac{4}{\\pi} \\approx 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Fehler",[888,5959,5960,6321,6932,6964],{},[891,5961,5962,5963,6061,6062,6117,6118,6215,6216,1181],{},"Den Vorfaktor falsch wählen. Er ist 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bei ",[573,6063,6065,6084],{"className":6064},[576],[573,6066,6068],{"className":6067},[580],[582,6069,6070],{"xmlns":584},[586,6071,6072,6082],{},[589,6073,6074,6076,6078,6080],{},[592,6075,920],{},[596,6077,1201],{},[725,6079,983],{},[592,6081,1206],{},[616,6083,1209],{"encoding":618},[573,6085,6087,6105],{"className":6086,"ariaHidden":624},[623],[573,6088,6090,6093,6096,6099,6102],{"className":6089},[628],[573,6091],{"className":6092,"style":1219},[632],[573,6094,920],{"className":6095,"style":954},[645,646],[573,6097],{"className":6098,"style":1226},[949],[573,6100,1201],{"className":6101},[1230],[573,6103],{"className":6104,"style":1226},[949],[573,6106,6108,6111,6114],{"className":6107},[628],[573,6109],{"className":6110,"style":739},[632],[573,6112,983],{"className":6113},[645],[573,6115,1206],{"className":6116,"style":647},[645,646]," also 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nicht ",[573,6217,6219,6241],{"className":6218},[576],[573,6220,6222],{"className":6221},[580],[582,6223,6224],{"xmlns":584},[586,6225,6226,6238],{},[589,6227,6228],{},[977,6229,6230,6232],{},[725,6231,1265],{},[589,6233,6234,6236],{},[725,6235,983],{},[592,6237,1206],{},[616,6239,6240],{"encoding":618},"\\frac{1}{2\\pi}",[573,6242,6244],{"className":6243,"ariaHidden":624},[623],[573,6245,6247,6250],{"className":6246},[628],[573,6248],{"className":6249,"style":1331},[632],[573,6251,6253,6256,6318],{"className":6252},[645],[573,6254],{"className":6255},[641,1030],[573,6257,6259],{"className":6258},[977],[573,6260,6262,6310],{"className":6261},[843,844],[573,6263,6265,6307],{"className":6264},[848],[573,6266,6268,6285,6293],{"className":6267,"style":1350},[852],[573,6269,6270,6273],{"style":1046},[573,6271],{"className":6272,"style":1050},[860],[573,6274,6276],{"className":6275},[865,866,867,868],[573,6277,6279,6282],{"className":6278},[645,868],[573,6280,983],{"className":6281},[645,868],[573,6283,1206],{"className":6284,"style":647},[645,646,868],[573,6286,6287,6290],{"style":1062},[573,6288],{"className":6289,"style":1050},[860],[573,6291],{"className":6292,"style":1070},[1069],[573,6294,6295,6298],{"style":1073},[573,6296],{"className":6297,"style":1050},[860],[573,6299,6301],{"className":6300},[865,866,867,868],[573,6302,6304],{"className":6303},[645,868],[573,6305,1265],{"className":6306},[645,868],[573,6308,876],{"className":6309},[875],[573,6311,6313],{"className":6312},[848],[573,6314,6316],{"className":6315,"style":1095},[852],[573,6317],{},[573,6319],{"className":6320},[655,1030],[891,6322,6323,6324,6394,6395,6493,6494,6563,6564,6703,6704,6215,6804,6833,6834,1181],{},"Bei 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den Faktor ",[573,6396,6398,6416],{"className":6397},[576],[573,6399,6401],{"className":6400},[580],[582,6402,6403],{"xmlns":584},[586,6404,6405,6413],{},[589,6406,6407],{},[977,6408,6409,6411],{},[725,6410,1265],{},[725,6412,983],{},[616,6414,6415],{"encoding":618},"\\frac{1}{2}",[573,6417,6419],{"className":6418,"ariaHidden":624},[623],[573,6420,6422,6425],{"className":6421},[628],[573,6423],{"className":6424,"style":1331},[632],[573,6426,6428,6431,6490],{"className":6427},[645],[573,6429],{"className":6430},[641,1030],[573,6432,6434],{"className":6433},[977],[573,6435,6437,6482],{"className":6436},[843,844],[573,6438,6440,6479],{"className":6439},[848],[573,6441,6443,6457,6465],{"className":6442,"style":1350},[852],[573,6444,6445,6448],{"style":1046},[573,6446],{"className":6447,"style":1050},[860],[573,6449,6451],{"className":6450},[865,866,867,868],[573,6452,6454],{"className":6453},[645,868],[573,6455,983],{"className":6456},[645,868],[573,6458,6459,6462],{"style":1062},[573,6460],{"className":6461,"style":1050},[860],[573,6463],{"className":6464,"style":1070},[1069],[573,6466,6467,6470],{"style":1073},[573,6468],{"className":6469,"style":1050},[860],[573,6471,6473],{"className":6472},[865,866,867,868],[573,6474,6476],{"className":6475},[645,868],[573,6477,1265],{"className":6478},[645,868],[573,6480,876],{"className":6481},[875],[573,6483,6485],{"className":6484},[848],[573,6486,6488],{"className":6487,"style":1095},[852],[573,6489],{},[573,6491],{"className":6492},[655,1030]," doppelt anwenden. Mit dieser Formel für 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steht in der Reihe ",[573,6565,6567,6589],{"className":6566},[576],[573,6568,6570],{"className":6569},[580],[582,6571,6572],{"xmlns":584},[586,6573,6574,6586],{},[589,6575,6576],{},[977,6577,6578,6584],{},[810,6579,6580,6582],{},[592,6581,814],{},[725,6583,727],{},[725,6585,983],{},[616,6587,6588],{"encoding":618},"\\frac{a_0}{2}",[573,6590,6592],{"className":6591,"ariaHidden":624},[623],[573,6593,6595,6598],{"className":6594},[628],[573,6596],{"className":6597,"style":1473},[632],[573,6599,6601,6604,6700],{"className":6600},[645],[573,6602],{"className":6603},[641,1030],[573,6605,6607],{"className":6606},[977],[573,6608,6610,6692],{"className":6609},[843,844],[573,6611,6613,6689],{"className":6612},[848],[573,6614,6616,6630,6638],{"className":6615,"style":1492},[852],[573,6617,6618,6621],{"style":1046},[573,6619],{"className":6620,"style":1050},[860],[573,6622,6624],{"className":6623},[865,866,867,868],[573,6625,6627],{"className":6626},[645,868],[573,6628,983],{"className":6629},[645,868],[573,6631,6632,6635],{"style":1062},[573,6633],{"className":6634,"style":1050},[860],[573,6636],{"className":6637,"style":1070},[1069],[573,6639,6640,6643],{"style":1517},[573,6641],{"className":6642,"style":1050},[860],[573,6644,6646],{"className":6645},[865,866,867,868],[573,6647,6649],{"className":6648},[645,868],[573,6650,6652,6655],{"className":6651},[645,868],[573,6653,814],{"className":6654},[645,646,868],[573,6656,6658],{"className":6657},[839],[573,6659,6661,6681],{"className":6660},[843,844],[573,6662,6664,6678],{"className":6663},[848],[573,6665,6667],{"className":6666,"style":1545},[852],[573,6668,6669,6672],{"style":1548},[573,6670],{"className":6671,"style":1552},[860],[573,6673,6675],{"className":6674},[865,1556,1020,868],[573,6676,727],{"className":6677},[645,868],[573,6679,876],{"className":6680},[875],[573,6682,6684],{"className":6683},[848],[573,6685,6687],{"className":6686,"style":1569},[852],[573,6688],{},[573,6690,876],{"className":6691},[875],[573,6693,6695],{"className":6694},[848],[573,6696,6698],{"className":6697,"style":1095},[852],[573,6699],{},[573,6701],{"className":6702},[655,1030],"; der Mittelwert der Dreieckschwingung ist ",[573,6705,6707,6725],{"className":6706},[576],[573,6708,6710],{"className":6709},[580],[582,6711,6712],{"xmlns":584},[586,6713,6714,6722],{},[589,6715,6716],{},[977,6717,6718,6720],{},[592,6719,1206],{},[725,6721,983],{},[616,6723,6724],{"encoding":618},"\\frac{\\pi}{2}",[573,6726,6728],{"className":6727,"ariaHidden":624},[623],[573,6729,6731,6735],{"className":6730},[628],[573,6732],{"className":6733,"style":6734},[632],"height:1.0404em;vertical-align:-0.345em;",[573,6736,6738,6741,6801],{"className":6737},[645],[573,6739],{"className":6740},[641,1030],[573,6742,6744],{"className":6743},[977],[573,6745,6747,6793],{"className":6746},[843,844],[573,6748,6750,6790],{"className":6749},[848],[573,6751,6754,6768,6776],{"className":6752,"style":6753},[852],"height:0.6954em;",[573,6755,6756,6759],{"style":1046},[573,6757],{"className":6758,"style":1050},[860],[573,6760,6762],{"className":6761},[865,866,867,868],[573,6763,6765],{"className":6764},[645,868],[573,6766,983],{"className":6767},[645,868],[573,6769,6770,6773],{"style":1062},[573,6771],{"className":6772,"style":1050},[860],[573,6774],{"className":6775,"style":1070},[1069],[573,6777,6778,6781],{"style":1073},[573,6779],{"className":6780,"style":1050},[860],[573,6782,6784],{"className":6783},[865,866,867,868],[573,6785,6787],{"className":6786},[645,868],[573,6788,1206],{"className":6789,"style":647},[645,646,868],[573,6791,876],{"className":6792},[875],[573,6794,6796],{"className":6795},[848],[573,6797,6799],{"className":6798,"style":1095},[852],[573,6800],{},[573,6802],{"className":6803},[655,1030],[573,6805,6807,6821],{"className":6806},[576],[573,6808,6810],{"className":6809},[580],[582,6811,6812],{"xmlns":584},[586,6813,6814,6818],{},[589,6815,6816],{},[592,6817,1206],{},[616,6819,6820],{"encoding":618},"\\pi",[573,6822,6824],{"className":6823,"ariaHidden":624},[623],[573,6825,6827,6830],{"className":6826},[628],[573,6828],{"className":6829,"style":1278},[632],[573,6831,1206],{"className":6832,"style":647},[645,646]," und nicht ",[573,6835,6837,6855],{"className":6836},[576],[573,6838,6840],{"className":6839},[580],[582,6841,6842],{"xmlns":584},[586,6843,6844,6852],{},[589,6845,6846],{},[977,6847,6848,6850],{},[592,6849,1206],{},[725,6851,3870],{},[616,6853,6854],{"encoding":618},"\\frac{\\pi}{4}",[573,6856,6858],{"className":6857,"ariaHidden":624},[623],[573,6859,6861,6864],{"className":6860},[628],[573,6862],{"className":6863,"style":6734},[632],[573,6865,6867,6870,6929],{"className":6866},[645],[573,6868],{"className":6869},[641,1030],[573,6871,6873],{"className":6872},[977],[573,6874,6876,6921],{"className":6875},[843,844],[573,6877,6879,6918],{"className":6878},[848],[573,6880,6882,6896,6904],{"className":6881,"style":6753},[852],[573,6883,6884,6887],{"style":1046},[573,6885],{"className":6886,"style":1050},[860],[573,6888,6890],{"className":6889},[865,866,867,868],[573,6891,6893],{"className":6892},[645,868],[573,6894,3870],{"className":6895},[645,868],[573,6897,6898,6901],{"style":1062},[573,6899],{"className":6900,"style":1050},[860],[573,6902],{"className":6903,"style":1070},[1069],[573,6905,6906,6909],{"style":1073},[573,6907],{"className":6908,"style":1050},[860],[573,6910,6912],{"className":6911},[865,866,867,868],[573,6913,6915],{"className":6914},[645,868],[573,6916,1206],{"className":6917,"style":647},[645,646,868],[573,6919,876],{"className":6920},[875],[573,6922,6924],{"className":6923},[848],[573,6925,6927],{"className":6926,"style":1095},[852],[573,6928],{},[573,6930],{"className":6931},[655,1030],[891,6933,6934,6935,6963],{},"Symmetrien nicht nutzen und lange Integrale ausrechnen, die ohnehin ",[573,6936,6938,6951],{"className":6937},[576],[573,6939,6941],{"className":6940},[580],[582,6942,6943],{"xmlns":584},[586,6944,6945,6949],{},[589,6946,6947],{},[725,6948,727],{},[616,6950,727],{"encoding":618},[573,6952,6954],{"className":6953,"ariaHidden":624},[623],[573,6955,6957,6960],{"className":6956},[628],[573,6958],{"className":6959,"style":739},[632],[573,6961,727],{"className":6962},[645]," ergeben.",[891,6965,6966],{},"Über ein Intervall integrieren, das keine volle Periode ist.",{"title":6968,"searchDepth":6969,"depth":6969,"links":6970},"",2,[6971,6972,6973],{"id":561,"depth":6969,"text":562},{"id":2696,"depth":6969,"text":2697},{"id":5956,"depth":6969,"text":5957},[6975,6977,6979,6982,6987,6990,6993,6996,6999,7001],{"lhs":6976,"rhs":727},"round(sum(map(0:999, f(k) = sin(2*(k + 0.5)*2*pi\u002F1000) * sin(3*(k + 0.5)*2*pi\u002F1000)))*2*pi\u002F1000, 6)",{"lhs":6978,"rhs":983},"round(sum(map(0:999, f(k) = (-pi + (k + 0.5)*2*pi\u002F1000) * sin(-pi + (k + 0.5)*2*pi\u002F1000)))*2\u002F1000, 4)",{"lhs":6980,"rhs":6981},"round(sum(map(0:999, f(k) = (-pi + (k + 0.5)*2*pi\u002F1000) * sin(2*(-pi + (k + 0.5)*2*pi\u002F1000))))*2\u002F1000, 4)","-1",{"lhs":6983,"rhs":6984,"where":6985},"2*(-1)^(n + 1)\u002Fn","2\u002F3",{"n":6986},3,{"lhs":6988,"rhs":6989},"(1\u002Fpi)*(pi^3\u002F3 - (-pi)^3\u002F3)","2*pi^2\u002F3",{"lhs":6991,"rhs":6992},"(2*pi^2\u002F3)\u002F4","pi^2\u002F6",{"lhs":6994,"rhs":6995},"round(sum(map(0:999, f(k) = abs(-pi + (k + 0.5)*2*pi\u002F1000)))*2\u002F1000, 4)","round(pi, 4)",{"lhs":6997,"rhs":6998},"round(sum(map(0:999, f(k) = abs(-pi + (k + 0.5)*2*pi\u002F1000) * cos(-pi + (k + 0.5)*2*pi\u002F1000)))*2\u002F1000, 4)","round(-4\u002Fpi, 4)",{"lhs":6998,"rhs":7000},"-1.2732",{"lhs":7002,"rhs":727,"where":7003},"2*((-1)^n - 1)\u002F(pi*n^2)",{"n":6969},"f\\ T\\text{-periodisch und über eine Periode integrierbar},\\ \\omega = \\tfrac{2\\pi}{T},\\ n \\geq 0 \\text{ für } a_n,\\ n \\geq 1 \\text{ für } b_n","\u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\\ T\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex\">-periodisch\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">und über eine Periode\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">integrierbar\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>ω\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmfrac>\u003Cmrow>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>π\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmfrac>\u003C\u002Fmstyle>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\omega = \\tfrac{2\\pi}{T},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">ω\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1901em;vertical-align:-0.345em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8451em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> 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class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">für\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","fourier-coefficients","a_n = \\frac{2}{T} \\int_{0}^{T} f(x) \\cos(n \\omega x)\\,dx,\\qquad b_n = \\frac{2}{T} \\int_{0}^{T} f(x) \\sin(n \\omega x)\\,dx","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>ω\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>ω\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_n = \\frac{2}{T} \\int_{0}^{T} f(x) \\cos(n \\omega x)\\,dx,\\qquad b_n = \\frac{2}{T} \\int_{0}^{T} f(x) \\sin(n \\omega x)\\,dx\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.5032em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.5912em;\">\u003Cspan style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8129em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9119em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan 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style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.5032em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.5912em;\">\u003Cspan style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8129em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9119em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">nω\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Ffourierkoeffizienten",[],[7017,7018,7019],"fourier-series","basel-problem","integration-by-parts",{"title":548,"description":6968},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Ffourierkoeffizienten","Die Fourierkoeffizienten aₙ und bₙ entstehen durch Integration von f mal cos(nωx) bzw. sin(nωx) über eine Periode.",[7024,7025,7026,7027],"fourierreihe","fourierkoeffizienten","integral","orthogonalität",[7029,7032,7036,7039,7042,7046,7049],{"symbol":819,"meaning":7030,"symbolHtml":7031},"Kosinuskoeffizienten (a₀\u002F2 ist der Mittelwert von f)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":7033,"meaning":7034,"symbolHtml":7035},"b_n","Sinuskoeffizienten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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