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ist der Mittelwert von ",[572,983,985,999],{"className":984},[575],[572,986,988],{"className":987},[579],[581,989,990],{"xmlns":583},[585,991,992,997],{},[588,993,994],{},[591,995,996],{},"f",[614,998,996],{"encoding":616},[572,1000,1002],{"className":1001,"ariaHidden":622},[621],[572,1003,1005,1009],{"className":1004},[626],[572,1006],{"className":1007,"style":1008},[630],"height:0.8889em;vertical-align:-0.1944em;",[572,1010,996],{"className":1011,"style":1012},[635,636],"margin-right:0.1076em;"," über eine Periode. Die Koeffizienten berechnet man mit den Formeln für die Fourierkoeffizienten.",[564,1015,1016,1017,1045,1046,1112,1113,1162,1163,1166],{},"Zur Konvergenz (Satz von Dirichlet): Ist ",[572,1018,1020,1033],{"className":1019},[575],[572,1021,1023],{"className":1022},[579],[581,1024,1025],{"xmlns":583},[585,1026,1027,1031],{},[588,1028,1029],{},[591,1030,996],{},[614,1032,996],{"encoding":616},[572,1034,1036],{"className":1035,"ariaHidden":622},[621],[572,1037,1039,1042],{"className":1038},[626],[572,1040],{"className":1041,"style":1008},[630],[572,1043,996],{"className":1044,"style":1012},[635,636]," stückweise stetig differenzierbar (stückweise ",[572,1047,1049,1070],{"className":1048},[575],[572,1050,1052],{"className":1051},[579],[581,1053,1054],{"xmlns":583},[585,1055,1056,1067],{},[588,1057,1058],{},[1059,1060,1061,1064],"msup",{},[591,1062,1063],{},"C",[604,1065,1066],{},"1",[614,1068,1069],{"encoding":616},"C^1",[572,1071,1073],{"className":1072,"ariaHidden":622},[621],[572,1074,1076,1080],{"className":1075},[626],[572,1077],{"className":1078,"style":1079},[630],"height:0.8141em;",[572,1081,1083,1087],{"className":1082},[635],[572,1084,1063],{"className":1085,"style":1086},[635,636],"margin-right:0.0715em;",[572,1088,1090],{"className":1089},[929],[572,1091,1093],{"className":1092},[671],[572,1094,1096],{"className":1095},[676],[572,1097,1099],{"className":1098,"style":1079},[680],[572,1100,1102,1106],{"style":1101},"top:-3.063em;margin-right:0.05em;",[572,1103],{"className":1104,"style":1105},[688],"height:2.7em;",[572,1107,1109],{"className":1108},[693,694,695,696],[572,1110,1066],{"className":1111},[635,696],"), konvergiert die Reihe an jeder Stetigkeitsstelle gegen ",[572,1114,1116,1140],{"className":1115},[575],[572,1117,1119],{"className":1118},[579],[581,1120,1121],{"xmlns":583},[585,1122,1123,1137],{},[588,1124,1125,1127,1131,1134],{},[591,1126,996],{},[595,1128,1130],{"stretchy":1129},"false","(",[591,1132,1133],{},"x",[595,1135,1136],{"stretchy":1129},")",[614,1138,1139],{"encoding":616},"f(x)",[572,1141,1143],{"className":1142,"ariaHidden":622},[621],[572,1144,1146,1150,1153,1156,1159],{"className":1145},[626],[572,1147],{"className":1148,"style":1149},[630],"height:1em;vertical-align:-0.25em;",[572,1151,996],{"className":1152,"style":1012},[635,636],[572,1154,1130],{"className":1155},[663],[572,1157,1133],{"className":1158},[635,636],[572,1160,1136],{"className":1161},[750],". An einer Sprungstelle konvergiert sie gegen den ",[568,1164,1165],{},"Mittelwert"," der beiden einseitigen Grenzwerte.",[564,1168,1169],{},"Symmetrien sparen Arbeit:",[1171,1172,1173,1309],"ul",{},[1174,1175,1176,1204,1205,1208,1209,1308],"li",{},[572,1177,1179,1192],{"className":1178},[575],[572,1180,1182],{"className":1181},[579],[581,1183,1184],{"xmlns":583},[585,1185,1186,1190],{},[588,1187,1188],{},[591,1189,996],{},[614,1191,996],{"encoding":616},[572,1193,1195],{"className":1194,"ariaHidden":622},[621],[572,1196,1198,1201],{"className":1197},[626],[572,1199],{"className":1200,"style":1008},[630],[572,1202,996],{"className":1203,"style":1012},[635,636]," ",[568,1206,1207],{},"gerade",": alle ",[572,1210,1212,1236],{"className":1211},[575],[572,1213,1215],{"className":1214},[579],[581,1216,1217],{"xmlns":583},[585,1218,1219,1233],{},[588,1220,1221,1229,1231],{},[844,1222,1223,1226],{},[591,1224,1225],{},"b",[591,1227,1228],{},"n",[595,1230,597],{},[604,1232,851],{},[614,1234,1235],{"encoding":616},"b_n = 0",[572,1237,1239,1298],{"className":1238,"ariaHidden":622},[621],[572,1240,1242,1246,1289,1292,1295],{"className":1241},[626],[572,1243],{"className":1244,"style":1245},[630],"height:0.8444em;vertical-align:-0.15em;",[572,1247,1249,1252],{"className":1248},[635],[572,1250,1225],{"className":1251},[635,636],[572,1253,1255],{"className":1254},[929],[572,1256,1258,1280],{"className":1257},[671,672],[572,1259,1261,1277],{"className":1260},[676],[572,1262,1265],{"className":1263,"style":1264},[680],"height:0.1514em;",[572,1266,1268,1271],{"style":1267},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[572,1269],{"className":1270,"style":1105},[688],[572,1272,1274],{"className":1273},[693,694,695,696],[572,1275,1228],{"className":1276},[635,636,696],[572,1278,737],{"className":1279},[736],[572,1281,1283],{"className":1282},[676],[572,1284,1287],{"className":1285,"style":1286},[680],"height:0.15em;",[572,1288],{},[572,1290],{"className":1291,"style":642},[641],[572,1293,597],{"className":1294},[646],[572,1296],{"className":1297,"style":642},[641],[572,1299,1301,1305],{"className":1300},[626],[572,1302],{"className":1303,"style":1304},[630],"height:0.6444em;",[572,1306,851],{"className":1307},[635],", es bleibt eine reine Kosinusreihe.",[1174,1310,1311,1204,1339,1208,1342,1435],{},[572,1312,1314,1327],{"className":1313},[575],[572,1315,1317],{"className":1316},[579],[581,1318,1319],{"xmlns":583},[585,1320,1321,1325],{},[588,1322,1323],{},[591,1324,996],{},[614,1326,996],{"encoding":616},[572,1328,1330],{"className":1329,"ariaHidden":622},[621],[572,1331,1333,1336],{"className":1332},[626],[572,1334],{"className":1335,"style":1008},[630],[572,1337,996],{"className":1338,"style":1012},[635,636],[568,1340,1341],{},"ungerade",[572,1343,1345,1367],{"className":1344},[575],[572,1346,1348],{"className":1347},[579],[581,1349,1350],{"xmlns":583},[585,1351,1352,1364],{},[588,1353,1354,1360,1362],{},[844,1355,1356,1358],{},[591,1357,848],{},[591,1359,1228],{},[595,1361,597],{},[604,1363,851],{},[614,1365,1366],{"encoding":616},"a_n = 0",[572,1368,1370,1426],{"className":1369,"ariaHidden":622},[621],[572,1371,1373,1377,1417,1420,1423],{"className":1372},[626],[572,1374],{"className":1375,"style":1376},[630],"height:0.5806em;vertical-align:-0.15em;",[572,1378,1380,1383],{"className":1379},[635],[572,1381,848],{"className":1382},[635,636],[572,1384,1386],{"className":1385},[929],[572,1387,1389,1409],{"className":1388},[671,672],[572,1390,1392,1406],{"className":1391},[676],[572,1393,1395],{"className":1394,"style":1264},[680],[572,1396,1397,1400],{"style":1267},[572,1398],{"className":1399,"style":1105},[688],[572,1401,1403],{"className":1402},[693,694,695,696],[572,1404,1228],{"className":1405},[635,636,696],[572,1407,737],{"className":1408},[736],[572,1410,1412],{"className":1411},[676],[572,1413,1415],{"className":1414,"style":1286},[680],[572,1416],{},[572,1418],{"className":1419,"style":642},[641],[572,1421,597],{"className":1422},[646],[572,1424],{"className":1425,"style":642},[641],[572,1427,1429,1432],{"className":1428},[626],[572,1430],{"className":1431,"style":1304},[630],[572,1433,851],{"className":1434},[635],", es bleibt eine reine Sinusreihe.",[564,1437,1438,1439,1699],{},"In der komplexen Form schreibt man ",[572,1440,1442,1508],{"className":1441},[575],[572,1443,1445],{"className":1444},[579],[581,1446,1447],{"xmlns":583},[585,1448,1449,1505],{},[588,1450,1451,1453,1455,1457,1459,1461,1482,1489],{},[591,1452,996],{},[595,1454,1130],{"stretchy":1129},[591,1456,1133],{},[595,1458,1136],{"stretchy":1129},[595,1460,597],{},[1462,1463,1464,1467,1480],"msubsup",{},[595,1465,1466],{},"∑",[588,1468,1469,1471,1473,1476],{},[591,1470,1228],{},[595,1472,597],{},[595,1474,1475],{},"−",[591,1477,1479],{"mathvariant":1478},"normal","∞",[591,1481,1479],{"mathvariant":1478},[844,1483,1484,1487],{},[591,1485,1486],{},"c",[591,1488,1228],{},[1059,1490,1491,1494],{},[591,1492,1493],{},"e",[588,1495,1496,1499,1501,1503],{},[591,1497,1498],{},"i",[591,1500,1228],{},[591,1502,593],{},[591,1504,1133],{},[614,1506,1507],{"encoding":616},"f(x) = \\sum_{n=-\\infty}^{\\infty} c_n e^{in\\omega x}",[572,1509,1511,1538],{"className":1510,"ariaHidden":622},[621],[572,1512,1514,1517,1520,1523,1526,1529,1532,1535],{"className":1513},[626],[572,1515],{"className":1516,"style":1149},[630],[572,1518,996],{"className":1519,"style":1012},[635,636],[572,1521,1130],{"className":1522},[663],[572,1524,1133],{"className":1525},[635,636],[572,1527,1136],{"className":1528},[750],[572,1530],{"className":1531,"style":642},[641],[572,1533,597],{"className":1534},[646],[572,1536],{"className":1537,"style":642},[641],[572,1539,1541,1545,1619,1622,1662],{"className":1540},[626],[572,1542],{"className":1543,"style":1544},[630],"height:1.1827em;vertical-align:-0.358em;",[572,1546,1549,1555],{"className":1547},[1548],"mop",[572,1550,1466],{"className":1551,"style":1554},[1548,1552,1553],"op-symbol","small-op","position:relative;top:0em;",[572,1556,1558],{"className":1557},[929],[572,1559,1561,1610],{"className":1560},[671,672],[572,1562,1564,1607],{"className":1563},[676],[572,1565,1568,1592],{"className":1566,"style":1567},[680],"height:0.8043em;",[572,1569,1571,1574],{"style":1570},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[572,1572],{"className":1573,"style":1105},[688],[572,1575,1577],{"className":1576},[693,694,695,696],[572,1578,1580,1583,1586,1589],{"className":1579},[635,696],[572,1581,1228],{"className":1582},[635,636,696],[572,1584,597],{"className":1585},[646,696],[572,1587,1475],{"className":1588},[635,696],[572,1590,1479],{"className":1591},[635,696],[572,1593,1595,1598],{"style":1594},"top:-3.2029em;margin-right:0.05em;",[572,1596],{"className":1597,"style":1105},[688],[572,1599,1601],{"className":1600},[693,694,695,696],[572,1602,1604],{"className":1603},[635,696],[572,1605,1479],{"className":1606},[635,696],[572,1608,737],{"className":1609},[736],[572,1611,1613],{"className":1612},[676],[572,1614,1617],{"className":1615,"style":1616},[680],"height:0.358em;",[572,1618],{},[572,1620],{"className":1621,"style":811},[641],[572,1623,1625,1628],{"className":1624},[635],[572,1626,1486],{"className":1627},[635,636],[572,1629,1631],{"className":1630},[929],[572,1632,1634,1654],{"className":1633},[671,672],[572,1635,1637,1651],{"className":1636},[676],[572,1638,1640],{"className":1639,"style":1264},[680],[572,1641,1642,1645],{"style":1267},[572,1643],{"className":1644,"style":1105},[688],[572,1646,1648],{"className":1647},[693,694,695,696],[572,1649,1228],{"className":1650},[635,636,696],[572,1652,737],{"className":1653},[736],[572,1655,1657],{"className":1656},[676],[572,1658,1660],{"className":1659,"style":1286},[680],[572,1661],{},[572,1663,1665,1668],{"className":1664},[635],[572,1666,1493],{"className":1667},[635,636],[572,1669,1671],{"className":1670},[929],[572,1672,1674],{"className":1673},[671],[572,1675,1677],{"className":1676},[676],[572,1678,1681],{"className":1679,"style":1680},[680],"height:0.8247em;",[572,1682,1683,1686],{"style":1101},[572,1684],{"className":1685,"style":1105},[688],[572,1687,1689],{"className":1688},[693,694,695,696],[572,1690,1692,1696],{"className":1691},[635,696],[572,1693,1695],{"className":1694,"style":637},[635,636,696],"inω",[572,1697,1133],{"className":1698},[635,636,696],". Anwendungen sind Signalverarbeitung, Akustik (Klangfarbe), Wärmeleitung und Schwingungen.",[559,1701,1703],{"id":1702},"beispiele","Beispiele",[564,1705,1706,1709,1710,1767,1768,1834,1835,751,1911,1834,1983,2062,2063,2091],{},[568,1707,1708],{},"Rechteckschwingung"," mit ",[572,1711,1713,1733],{"className":1712},[575],[572,1714,1716],{"className":1715},[579],[581,1717,1718],{"xmlns":583},[585,1719,1720,1730],{},[588,1721,1722,1724,1726,1728],{},[591,1723,612],{},[595,1725,597],{},[604,1727,606],{},[591,1729,609],{},[614,1731,1732],{"encoding":616},"T = 2\\pi",[572,1734,1736,1755],{"className":1735,"ariaHidden":622},[621],[572,1737,1739,1743,1746,1749,1752],{"className":1738},[626],[572,1740],{"className":1741,"style":1742},[630],"height:0.6833em;",[572,1744,612],{"className":1745,"style":703},[635,636],[572,1747],{"className":1748,"style":642},[641],[572,1750,597],{"className":1751},[646],[572,1753],{"className":1754,"style":642},[641],[572,1756,1758,1761,1764],{"className":1757},[626],[572,1759],{"className":1760,"style":1304},[630],[572,1762,606],{"className":1763},[635],[572,1765,609],{"className":1766,"style":637},[635,636],": ",[572,1769,1771,1795],{"className":1770},[575],[572,1772,1774],{"className":1773},[579],[581,1775,1776],{"xmlns":583},[585,1777,1778,1792],{},[588,1779,1780,1782,1784,1786,1788,1790],{},[591,1781,996],{},[595,1783,1130],{"stretchy":1129},[591,1785,1133],{},[595,1787,1136],{"stretchy":1129},[595,1789,597],{},[604,1791,1066],{},[614,1793,1794],{"encoding":616},"f(x) = 1",[572,1796,1798,1825],{"className":1797,"ariaHidden":622},[621],[572,1799,1801,1804,1807,1810,1813,1816,1819,1822],{"className":1800},[626],[572,1802],{"className":1803,"style":1149},[630],[572,1805,996],{"className":1806,"style":1012},[635,636],[572,1808,1130],{"className":1809},[663],[572,1811,1133],{"className":1812},[635,636],[572,1814,1136],{"className":1815},[750],[572,1817],{"className":1818,"style":642},[641],[572,1820,597],{"className":1821},[646],[572,1823],{"className":1824,"style":642},[641],[572,1826,1828,1831],{"className":1827},[626],[572,1829],{"className":1830,"style":1304},[630],[572,1832,1066],{"className":1833},[635]," für ",[572,1836,1838,1861],{"className":1837},[575],[572,1839,1841],{"className":1840},[579],[581,1842,1843],{"xmlns":583},[585,1844,1845,1858],{},[588,1846,1847,1849,1852,1854,1856],{},[604,1848,851],{},[595,1850,1851],{},"\u003C",[591,1853,1133],{},[595,1855,1851],{},[591,1857,609],{},[614,1859,1860],{"encoding":616},"0 \u003C x \u003C \\pi",[572,1862,1864,1883,1902],{"className":1863,"ariaHidden":622},[621],[572,1865,1867,1871,1874,1877,1880],{"className":1866},[626],[572,1868],{"className":1869,"style":1870},[630],"height:0.6835em;vertical-align:-0.0391em;",[572,1872,851],{"className":1873},[635],[572,1875],{"className":1876,"style":642},[641],[572,1878,1851],{"className":1879},[646],[572,1881],{"className":1882,"style":642},[641],[572,1884,1886,1890,1893,1896,1899],{"className":1885},[626],[572,1887],{"className":1888,"style":1889},[630],"height:0.5782em;vertical-align:-0.0391em;",[572,1891,1133],{"className":1892},[635,636],[572,1894],{"className":1895,"style":642},[641],[572,1897,1851],{"className":1898},[646],[572,1900],{"className":1901,"style":642},[641],[572,1903,1905,1908],{"className":1904},[626],[572,1906],{"className":1907,"style":631},[630],[572,1909,609],{"className":1910,"style":637},[635,636],[572,1912,1914,1940],{"className":1913},[575],[572,1915,1917],{"className":1916},[579],[581,1918,1919],{"xmlns":583},[585,1920,1921,1937],{},[588,1922,1923,1925,1927,1929,1931,1933,1935],{},[591,1924,996],{},[595,1926,1130],{"stretchy":1129},[591,1928,1133],{},[595,1930,1136],{"stretchy":1129},[595,1932,597],{},[595,1934,1475],{},[604,1936,1066],{},[614,1938,1939],{"encoding":616},"f(x) = -1",[572,1941,1943,1970],{"className":1942,"ariaHidden":622},[621],[572,1944,1946,1949,1952,1955,1958,1961,1964,1967],{"className":1945},[626],[572,1947],{"className":1948,"style":1149},[630],[572,1950,996],{"className":1951,"style":1012},[635,636],[572,1953,1130],{"className":1954},[663],[572,1956,1133],{"className":1957},[635,636],[572,1959,1136],{"className":1960},[750],[572,1962],{"className":1963,"style":642},[641],[572,1965,597],{"className":1966},[646],[572,1968],{"className":1969,"style":642},[641],[572,1971,1973,1977,1980],{"className":1972},[626],[572,1974],{"className":1975,"style":1976},[630],"height:0.7278em;vertical-align:-0.0833em;",[572,1978,1475],{"className":1979},[635],[572,1981,1066],{"className":1982},[635],[572,1984,1986,2010],{"className":1985},[575],[572,1987,1989],{"className":1988},[579],[581,1990,1991],{"xmlns":583},[585,1992,1993,2007],{},[588,1994,1995,1997,1999,2001,2003,2005],{},[595,1996,1475],{},[591,1998,609],{},[595,2000,1851],{},[591,2002,1133],{},[595,2004,1851],{},[604,2006,851],{},[614,2008,2009],{"encoding":616},"-\\pi \u003C x \u003C 0",[572,2011,2013,2035,2053],{"className":2012,"ariaHidden":622},[621],[572,2014,2016,2020,2023,2026,2029,2032],{"className":2015},[626],[572,2017],{"className":2018,"style":2019},[630],"height:0.6667em;vertical-align:-0.0833em;",[572,2021,1475],{"className":2022},[635],[572,2024,609],{"className":2025,"style":637},[635,636],[572,2027],{"className":2028,"style":642},[641],[572,2030,1851],{"className":2031},[646],[572,2033],{"className":2034,"style":642},[641],[572,2036,2038,2041,2044,2047,2050],{"className":2037},[626],[572,2039],{"className":2040,"style":1889},[630],[572,2042,1133],{"className":2043},[635,636],[572,2045],{"className":2046,"style":642},[641],[572,2048,1851],{"className":2049},[646],[572,2051],{"className":2052,"style":642},[641],[572,2054,2056,2059],{"className":2055},[626],[572,2057],{"className":2058,"style":1304},[630],[572,2060,851],{"className":2061},[635],". Die Funktion ist ungerade, und nur ungerade ",[572,2064,2066,2079],{"className":2065},[575],[572,2067,2069],{"className":2068},[579],[581,2070,2071],{"xmlns":583},[585,2072,2073,2077],{},[588,2074,2075],{},[591,2076,1228],{},[614,2078,1228],{"encoding":616},[572,2080,2082],{"className":2081,"ariaHidden":622},[621],[572,2083,2085,2088],{"className":2084},[626],[572,2086],{"className":2087,"style":631},[630],[572,2089,1228],{"className":2090},[635,636]," tragen bei:",[572,2093,2096],{"className":2094},[2095],"katex-display",[572,2097,2099,2186],{"className":2098},[575],[572,2100,2102],{"className":2101},[579],[581,2103,2105],{"xmlns":583,"display":2104},"block",[585,2106,2107,2183],{},[588,2108,2109,2111,2113,2115,2117,2119,2126],{},[591,2110,996],{},[595,2112,1130],{"stretchy":1129},[591,2114,1133],{},[595,2116,1136],{"stretchy":1129},[595,2118,597],{},[599,2120,2121,2124],{},[604,2122,2123],{},"4",[591,2125,609],{},[588,2127,2128,2130,2133,2136,2138,2141,2155,2157,2172,2174,2177,2181],{},[595,2129,1130],{"fence":622},[591,2131,2132],{},"sin",[595,2134,2135],{},"⁡",[591,2137,1133],{},[595,2139,2140],{},"+",[599,2142,2143,2153],{},[588,2144,2145,2147,2149,2151],{},[591,2146,2132],{},[595,2148,2135],{},[604,2150,777],{},[591,2152,1133],{},[604,2154,777],{},[595,2156,2140],{},[599,2158,2159,2170],{},[588,2160,2161,2163,2165,2168],{},[591,2162,2132],{},[595,2164,2135],{},[604,2166,2167],{},"5",[591,2169,1133],{},[604,2171,2167],{},[595,2173,2140],{},[595,2175,2176],{},"⋯",[2178,2179,2180],"mtext",{}," ",[595,2182,1136],{"fence":622},[614,2184,2185],{"encoding":616},"f(x) = \\frac{4}{\\pi} \\left( \\sin x + \\frac{\\sin 3x}{3} + \\frac{\\sin 5x}{5} + \\cdots \\right)",[572,2187,2189,2216],{"className":2188,"ariaHidden":622},[621],[572,2190,2192,2195,2198,2201,2204,2207,2210,2213],{"className":2191},[626],[572,2193],{"className":2194,"style":1149},[630],[572,2196,996],{"className":2197,"style":1012},[635,636],[572,2199,1130],{"className":2200},[663],[572,2202,1133],{"className":2203},[635,636],[572,2205,1136],{"className":2206},[750],[572,2208],{"className":2209,"style":642},[641],[572,2211,597],{"className":2212},[646],[572,2214],{"className":2215,"style":642},[641],[572,2217,2219,2223,2289,2292],{"className":2218},[626],[572,2220],{"className":2221,"style":2222},[630],"height:2.4em;vertical-align:-0.95em;",[572,2224,2226,2229,2286],{"className":2225},[635],[572,2227],{"className":2228},[663,664],[572,2230,2232],{"className":2231},[599],[572,2233,2235,2277],{"className":2234},[671,672],[572,2236,2238,2274],{"className":2237},[676],[572,2239,2242,2254,2262],{"className":2240,"style":2241},[680],"height:1.3214em;",[572,2243,2245,2248],{"style":2244},"top:-2.314em;",[572,2246],{"className":2247,"style":689},[688],[572,2249,2251],{"className":2250},[635],[572,2252,609],{"className":2253,"style":637},[635,636],[572,2255,2256,2259],{"style":706},[572,2257],{"className":2258,"style":689},[688],[572,2260],{"className":2261,"style":714},[713],[572,2263,2265,2268],{"style":2264},"top:-3.677em;",[572,2266],{"className":2267,"style":689},[688],[572,2269,2271],{"className":2270},[635],[572,2272,2123],{"className":2273},[635],[572,2275,737],{"className":2276},[736],[572,2278,2280],{"className":2279},[676],[572,2281,2284],{"className":2282,"style":2283},[680],"height:0.686em;",[572,2285],{},[572,2287],{"className":2288},[750,664],[572,2290],{"className":2291,"style":811},[641],[572,2293,2295,2304,2307,2310,2313,2317,2321,2324,2396,2399,2402,2405,2476,2479,2482,2485,2488,2491],{"className":2294},[827],[572,2296,2300],{"className":2297,"style":2299},[663,2298],"delimcenter","top:0em;",[572,2301,1130],{"className":2302},[2303,695],"delimsizing",[572,2305,2132],{"className":2306},[1548],[572,2308],{"className":2309,"style":811},[641],[572,2311,1133],{"className":2312},[635,636],[572,2314],{"className":2315,"style":2316},[641],"margin-right:0.2222em;",[572,2318,2140],{"className":2319},[2320],"mbin",[572,2322],{"className":2323,"style":2316},[641],[572,2325,2327,2330,2393],{"className":2326},[635],[572,2328],{"className":2329},[663,664],[572,2331,2333],{"className":2332},[599],[572,2334,2336,2385],{"className":2335},[671,672],[572,2337,2339,2382],{"className":2338},[676],[572,2340,2343,2354,2362],{"className":2341,"style":2342},[680],"height:1.3449em;",[572,2344,2345,2348],{"style":2244},[572,2346],{"className":2347,"style":689},[688],[572,2349,2351],{"className":2350},[635],[572,2352,777],{"className":2353},[635],[572,2355,2356,2359],{"style":706},[572,2357],{"className":2358,"style":689},[688],[572,2360],{"className":2361,"style":714},[713],[572,2363,2364,2367],{"style":2264},[572,2365],{"className":2366,"style":689},[688],[572,2368,2370,2373,2376,2379],{"className":2369},[635],[572,2371,2132],{"className":2372},[1548],[572,2374],{"className":2375,"style":811},[641],[572,2377,777],{"className":2378},[635],[572,2380,1133],{"className":2381},[635,636],[572,2383,737],{"className":2384},[736],[572,2386,2388],{"className":2387},[676],[572,2389,2391],{"className":2390,"style":2283},[680],[572,2392],{},[572,2394],{"className":2395},[750,664],[572,2397],{"className":2398,"style":2316},[641],[572,2400,2140],{"className":2401},[2320],[572,2403],{"className":2404,"style":2316},[641],[572,2406,2408,2411,2473],{"className":2407},[635],[572,2409],{"className":2410},[663,664],[572,2412,2414],{"className":2413},[599],[572,2415,2417,2465],{"className":2416},[671,672],[572,2418,2420,2462],{"className":2419},[676],[572,2421,2423,2434,2442],{"className":2422,"style":2342},[680],[572,2424,2425,2428],{"style":2244},[572,2426],{"className":2427,"style":689},[688],[572,2429,2431],{"className":2430},[635],[572,2432,2167],{"className":2433},[635],[572,2435,2436,2439],{"style":706},[572,2437],{"className":2438,"style":689},[688],[572,2440],{"className":2441,"style":714},[713],[572,2443,2444,2447],{"style":2264},[572,2445],{"className":2446,"style":689},[688],[572,2448,2450,2453,2456,2459],{"className":2449},[635],[572,2451,2132],{"className":2452},[1548],[572,2454],{"className":2455,"style":811},[641],[572,2457,2167],{"className":2458},[635],[572,2460,1133],{"className":2461},[635,636],[572,2463,737],{"className":2464},[736],[572,2466,2468],{"className":2467},[676],[572,2469,2471],{"className":2470,"style":2283},[680],[572,2472],{},[572,2474],{"className":2475},[750,664],[572,2477],{"className":2478,"style":2316},[641],[572,2480,2140],{"className":2481},[2320],[572,2483],{"className":2484,"style":2316},[641],[572,2486,2176],{"className":2487},[827],[572,2489],{"className":2490,"style":811},[641],[572,2492,2494],{"className":2493,"style":2299},[750,2298],[572,2495,1136],{"className":2496},[2303,695],[564,2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",[572,2501,2503,2525],{"className":2502},[575],[572,2504,2506],{"className":2505},[579],[581,2507,2508],{"xmlns":583},[585,2509,2510,2522],{},[588,2511,2512,2514,2516],{},[591,2513,1133],{},[595,2515,597],{},[599,2517,2518,2520],{},[591,2519,609],{},[604,2521,606],{},[614,2523,2524],{"encoding":616},"x = \\frac{\\pi}{2}",[572,2526,2528,2546],{"className":2527,"ariaHidden":622},[621],[572,2529,2531,2534,2537,2540,2543],{"className":2530},[626],[572,2532],{"className":2533,"style":631},[630],[572,2535,1133],{"className":2536},[635,636],[572,2538],{"className":2539,"style":642},[641],[572,2541,597],{"className":2542},[646],[572,2544],{"className":2545,"style":642},[641],[572,2547,2549,2553],{"className":2548},[626],[572,2550],{"className":2551,"style":2552},[630],"height:1.0404em;vertical-align:-0.345em;",[572,2554,2556,2559,2619],{"className":2555},[635],[572,2557],{"className":2558},[663,664],[572,2560,2562],{"className":2561},[599],[572,2563,2565,2611],{"className":2564},[671,672],[572,2566,2568,2608],{"className":2567},[676],[572,2569,2572,2586,2594],{"className":2570,"style":2571},[680],"height:0.6954em;",[572,2573,2574,2577],{"style":684},[572,2575],{"className":2576,"style":689},[688],[572,2578,2580],{"className":2579},[693,694,695,696],[572,2581,2583],{"className":2582},[635,696],[572,2584,606],{"className":2585},[635,696],[572,2587,2588,2591],{"style":706},[572,2589],{"className":2590,"style":689},[688],[572,2592],{"className":2593,"style":714},[713],[572,2595,2596,2599],{"style":717},[572,2597],{"className":2598,"style":689},[688],[572,2600,2602],{"className":2601},[693,694,695,696],[572,2603,2605],{"className":2604},[635,696],[572,2606,609],{"className":2607,"style":637},[635,636,696],[572,2609,737],{"className":2610},[736],[572,2612,2614],{"className":2613},[676],[572,2615,2617],{"className":2616,"style":744},[680],[572,2618],{},[572,2620],{"className":2621},[750,664]," ist ",[572,2624,2626,2644],{"className":2625},[575],[572,2627,2629],{"className":2628},[579],[581,2630,2631],{"xmlns":583},[585,2632,2633,2641],{},[588,2634,2635,2637,2639],{},[591,2636,996],{},[595,2638,597],{},[604,2640,1066],{},[614,2642,2643],{"encoding":616},"f = 1",[572,2645,2647,2665],{"className":2646,"ariaHidden":622},[621],[572,2648,2650,2653,2656,2659,2662],{"className":2649},[626],[572,2651],{"className":2652,"style":1008},[630],[572,2654,996],{"className":2655,"style":1012},[635,636],[572,2657],{"className":2658,"style":642},[641],[572,2660,597],{"className":2661},[646],[572,2663],{"className":2664,"style":642},[641],[572,2666,2668,2671],{"className":2667},[626],[572,2669],{"className":2670,"style":1304},[630],[572,2672,1066],{"className":2673},[635],", und es entsteht die Leibniz-Reihe ",[572,2676,2678,2720],{"className":2677},[575],[572,2679,2681],{"className":2680},[579],[581,2682,2683],{"xmlns":583},[585,2684,2685,2717],{},[588,2686,2687,2689,2691,2697,2699,2705,2707,2709,2711],{},[604,2688,1066],{},[595,2690,1475],{},[599,2692,2693,2695],{},[604,2694,1066],{},[604,2696,777],{},[595,2698,2140],{},[599,2700,2701,2703],{},[604,2702,1066],{},[604,2704,2167],{},[595,2706,1475],{},[595,2708,2176],{},[595,2710,597],{},[599,2712,2713,2715],{},[591,2714,609],{},[604,2716,2123],{},[614,2718,2719],{"encoding":616},"1 - \\frac{1}{3} + \\frac{1}{5} - \\cdots = \\frac{\\pi}{4}",[572,2721,2723,2741,2824,2907,2926],{"className":2722,"ariaHidden":622},[621],[572,2724,2726,2729,2732,2735,2738],{"className":2725},[626],[572,2727],{"className":2728,"style":1976},[630],[572,2730,1066],{"className":2731},[635],[572,2733],{"className":2734,"style":2316},[641],[572,2736,1475],{"className":2737},[2320],[572,2739],{"className":2740,"style":2316},[641],[572,2742,2744,2747,2815,2818,2821],{"className":2743},[626],[572,2745],{"className":2746,"style":656},[630],[572,2748,2750,2753,2812],{"className":2749},[635],[572,2751],{"className":2752},[663,664],[572,2754,2756],{"className":2755},[599],[572,2757,2759,2804],{"className":2758},[671,672],[572,2760,2762,2801],{"className":2761},[676],[572,2763,2765,2779,2787],{"className":2764,"style":681},[680],[572,2766,2767,2770],{"style":684},[572,2768],{"className":2769,"style":689},[688],[572,2771,2773],{"className":2772},[693,694,695,696],[572,2774,2776],{"className":2775},[635,696],[572,2777,777],{"className":2778},[635,696],[572,2780,2781,2784],{"style":706},[572,2782],{"className":2783,"style":689},[688],[572,2785],{"className":2786,"style":714},[713],[572,2788,2789,2792],{"style":717},[572,2790],{"className":2791,"style":689},[688],[572,2793,2795],{"className":2794},[693,694,695,696],[572,2796,2798],{"className":2797},[635,696],[572,2799,1066],{"className":2800},[635,696],[572,2802,737],{"className":2803},[736],[572,2805,2807],{"className":2806},[676],[572,2808,2810],{"className":2809,"style":744},[680],[572,2811],{},[572,2813],{"className":2814},[750,664],[572,2816],{"className":2817,"style":2316},[641],[572,2819,2140],{"className":2820},[2320],[572,2822],{"className":2823,"style":2316},[641],[572,2825,2827,2830,2898,2901,2904],{"className":2826},[626],[572,2828],{"className":2829,"style":656},[630],[572,2831,2833,2836,2895],{"className":2832},[635],[572,2834],{"className":2835},[663,664],[572,2837,2839],{"className":2838},[599],[572,2840,2842,2887],{"className":2841},[671,672],[572,2843,2845,2884],{"className":2844},[676],[572,2846,2848,2862,2870],{"className":2847,"style":681},[680],[572,2849,2850,2853],{"style":684},[572,2851],{"className":2852,"style":689},[688],[572,2854,2856],{"className":2855},[693,694,695,696],[572,2857,2859],{"className":2858},[635,696],[572,2860,2167],{"className":2861},[635,696],[572,2863,2864,2867],{"style":706},[572,2865],{"className":2866,"style":689},[688],[572,2868],{"className":2869,"style":714},[713],[572,2871,2872,2875],{"style":717},[572,2873],{"className":2874,"style":689},[688],[572,2876,2878],{"className":2877},[693,694,695,696],[572,2879,2881],{"className":2880},[635,696],[572,2882,1066],{"className":2883},[635,696],[572,2885,737],{"className":2886},[736],[572,2888,2890],{"className":2889},[676],[572,2891,2893],{"className":2892,"style":744},[680],[572,2894],{},[572,2896],{"className":2897},[750,664],[572,2899],{"className":2900,"style":2316},[641],[572,2902,1475],{"className":2903},[2320],[572,2905],{"className":2906,"style":2316},[641],[572,2908,2910,2914,2917,2920,2923],{"className":2909},[626],[572,2911],{"className":2912,"style":2913},[630],"height:0.3669em;",[572,2915,2176],{"className":2916},[827],[572,2918],{"className":2919,"style":642},[641],[572,2921,597],{"className":2922},[646],[572,2924],{"className":2925,"style":642},[641],[572,2927,2929,2932],{"className":2928},[626],[572,2930],{"className":2931,"style":2552},[630],[572,2933,2935,2938,2997],{"className":2934},[635],[572,2936],{"className":2937},[663,664],[572,2939,2941],{"className":2940},[599],[572,2942,2944,2989],{"className":2943},[671,672],[572,2945,2947,2986],{"className":2946},[676],[572,2948,2950,2964,2972],{"className":2949,"style":2571},[680],[572,2951,2952,2955],{"style":684},[572,2953],{"className":2954,"style":689},[688],[572,2956,2958],{"className":2957},[693,694,695,696],[572,2959,2961],{"className":2960},[635,696],[572,2962,2123],{"className":2963},[635,696],[572,2965,2966,2969],{"style":706},[572,2967],{"className":2968,"style":689},[688],[572,2970],{"className":2971,"style":714},[713],[572,2973,2974,2977],{"style":717},[572,2975],{"className":2976,"style":689},[688],[572,2978,2980],{"className":2979},[693,694,695,696],[572,2981,2983],{"className":2982},[635,696],[572,2984,609],{"className":2985,"style":637},[635,636,696],[572,2987,737],{"className":2988},[736],[572,2990,2992],{"className":2991},[676],[572,2993,2995],{"className":2994,"style":744},[680],[572,2996],{},[572,2998],{"className":2999},[750,664],". Bei ",[572,3002,3004,3022],{"className":3003},[575],[572,3005,3007],{"className":3006},[579],[581,3008,3009],{"xmlns":583},[585,3010,3011,3019],{},[588,3012,3013,3015,3017],{},[591,3014,1133],{},[595,3016,597],{},[604,3018,851],{},[614,3020,3021],{"encoding":616},"x = 0",[572,3023,3025,3043],{"className":3024,"ariaHidden":622},[621],[572,3026,3028,3031,3034,3037,3040],{"className":3027},[626],[572,3029],{"className":3030,"style":631},[630],[572,3032,1133],{"className":3033},[635,636],[572,3035],{"className":3036,"style":642},[641],[572,3038,597],{"className":3039},[646],[572,3041],{"className":3042,"style":642},[641],[572,3044,3046,3049],{"className":3045},[626],[572,3047],{"className":3048,"style":1304},[630],[572,3050,851],{"className":3051},[635]," springt ",[572,3054,3056,3069],{"className":3055},[575],[572,3057,3059],{"className":3058},[579],[581,3060,3061],{"xmlns":583},[585,3062,3063,3067],{},[588,3064,3065],{},[591,3066,996],{},[614,3068,996],{"encoding":616},[572,3070,3072],{"className":3071,"ariaHidden":622},[621],[572,3073,3075,3078],{"className":3074},[626],[572,3076],{"className":3077,"style":1008},[630],[572,3079,996],{"className":3080,"style":1012},[635,636]," von ",[572,3083,3085,3101],{"className":3084},[575],[572,3086,3088],{"className":3087},[579],[581,3089,3090],{"xmlns":583},[585,3091,3092,3098],{},[588,3093,3094,3096],{},[595,3095,1475],{},[604,3097,1066],{},[614,3099,3100],{"encoding":616},"-1",[572,3102,3104],{"className":3103,"ariaHidden":622},[621],[572,3105,3107,3110,3113],{"className":3106},[626],[572,3108],{"className":3109,"style":1976},[630],[572,3111,1475],{"className":3112},[635],[572,3114,1066],{"className":3115},[635]," auf ",[572,3118,3120,3133],{"className":3119},[575],[572,3121,3123],{"className":3122},[579],[581,3124,3125],{"xmlns":583},[585,3126,3127,3131],{},[588,3128,3129],{},[604,3130,1066],{},[614,3132,1066],{"encoding":616},[572,3134,3136],{"className":3135,"ariaHidden":622},[621],[572,3137,3139,3142],{"className":3138},[626],[572,3140],{"className":3141,"style":1304},[630],[572,3143,1066],{"className":3144},[635],"; die Reihe liefert dort ",[572,3147,3149,3162],{"className":3148},[575],[572,3150,3152],{"className":3151},[579],[581,3153,3154],{"xmlns":583},[585,3155,3156,3160],{},[588,3157,3158],{},[604,3159,851],{},[614,3161,851],{"encoding":616},[572,3163,3165],{"className":3164,"ariaHidden":622},[621],[572,3166,3168,3171],{"className":3167},[626],[572,3169],{"className":3170,"style":1304},[630],[572,3172,851],{"className":3173},[635],", den Mittelwert.",[564,3176,3177,1204,3180,3116,3246,3303],{},[568,3178,3179],{},"Sägezahn",[572,3181,3183,3207],{"className":3182},[575],[572,3184,3186],{"className":3185},[579],[581,3187,3188],{"xmlns":583},[585,3189,3190,3204],{},[588,3191,3192,3194,3196,3198,3200,3202],{},[591,3193,996],{},[595,3195,1130],{"stretchy":1129},[591,3197,1133],{},[595,3199,1136],{"stretchy":1129},[595,3201,597],{},[591,3203,1133],{},[614,3205,3206],{"encoding":616},"f(x) = x",[572,3208,3210,3237],{"className":3209,"ariaHidden":622},[621],[572,3211,3213,3216,3219,3222,3225,3228,3231,3234],{"className":3212},[626],[572,3214],{"className":3215,"style":1149},[630],[572,3217,996],{"className":3218,"style":1012},[635,636],[572,3220,1130],{"className":3221},[663],[572,3223,1133],{"className":3224},[635,636],[572,3226,1136],{"className":3227},[750],[572,3229],{"className":3230,"style":642},[641],[572,3232,597],{"className":3233},[646],[572,3235],{"className":3236,"style":642},[641],[572,3238,3240,3243],{"className":3239},[626],[572,3241],{"className":3242,"style":631},[630],[572,3244,1133],{"className":3245},[635,636],[572,3247,3249,3273],{"className":3248},[575],[572,3250,3252],{"className":3251},[579],[581,3253,3254],{"xmlns":583},[585,3255,3256,3270],{},[588,3257,3258,3260,3262,3264,3266,3268],{},[595,3259,1130],{"stretchy":1129},[595,3261,1475],{},[591,3263,609],{},[595,3265,774],{"separator":622},[591,3267,609],{},[595,3269,1136],{"stretchy":1129},[614,3271,3272],{"encoding":616},"(-\\pi, \\pi)",[572,3274,3276],{"className":3275,"ariaHidden":622},[621],[572,3277,3279,3282,3285,3288,3291,3294,3297,3300],{"className":3278},[626],[572,3280],{"className":3281,"style":1149},[630],[572,3283,1130],{"className":3284},[663],[572,3286,1475],{"className":3287},[635],[572,3289,609],{"className":3290,"style":637},[635,636],[572,3292,774],{"className":3293},[807],[572,3295],{"className":3296,"style":811},[641],[572,3298,609],{"className":3299,"style":637},[635,636],[572,3301,1136],{"className":3302},[750],", periodisch fortgesetzt:",[572,3305,3307],{"className":3306},[2095],[572,3308,3310,3378],{"className":3309},[575],[572,3311,3313],{"className":3312},[579],[581,3314,3315],{"xmlns":583,"display":2104},[585,3316,3317,3375],{},[588,3318,3319,3321,3323,3325],{},[591,3320,1133],{},[595,3322,597],{},[604,3324,606],{},[588,3326,3327,3329,3331,3333,3335,3337,3351,3353,3367,3369,3371,3373],{},[595,3328,1130],{"fence":622},[591,3330,2132],{},[595,3332,2135],{},[591,3334,1133],{},[595,3336,1475],{},[599,3338,3339,3349],{},[588,3340,3341,3343,3345,3347],{},[591,3342,2132],{},[595,3344,2135],{},[604,3346,606],{},[591,3348,1133],{},[604,3350,606],{},[595,3352,2140],{},[599,3354,3355,3365],{},[588,3356,3357,3359,3361,3363],{},[591,3358,2132],{},[595,3360,2135],{},[604,3362,777],{},[591,3364,1133],{},[604,3366,777],{},[595,3368,1475],{},[595,3370,2176],{},[2178,3372,2180],{},[595,3374,1136],{"fence":622},[614,3376,3377],{"encoding":616},"x = 2 \\left( \\sin x - \\frac{\\sin 2x}{2} + \\frac{\\sin 3x}{3} - \\cdots \\right)",[572,3379,3381,3399],{"className":3380,"ariaHidden":622},[621],[572,3382,3384,3387,3390,3393,3396],{"className":3383},[626],[572,3385],{"className":3386,"style":631},[630],[572,3388,1133],{"className":3389},[635,636],[572,3391],{"className":3392,"style":642},[641],[572,3394,597],{"className":3395},[646],[572,3397],{"className":3398,"style":642},[641],[572,3400,3402,3405,3408,3411],{"className":3401},[626],[572,3403],{"className":3404,"style":2222},[630],[572,3406,606],{"className":3407},[635],[572,3409],{"className":3410,"style":811},[641],[572,3412,3414,3420,3423,3426,3429,3432,3435,3438,3509,3512,3515,3518,3589,3592,3595,3598,3601,3604],{"className":3413},[827],[572,3415,3417],{"className":3416,"style":2299},[663,2298],[572,3418,1130],{"className":3419},[2303,695],[572,3421,2132],{"className":3422},[1548],[572,3424],{"className":3425,"style":811},[641],[572,3427,1133],{"className":3428},[635,636],[572,3430],{"className":3431,"style":2316},[641],[572,3433,1475],{"className":3434},[2320],[572,3436],{"className":3437,"style":2316},[641],[572,3439,3441,3444,3506],{"className":3440},[635],[572,3442],{"className":3443},[663,664],[572,3445,3447],{"className":3446},[599],[572,3448,3450,3498],{"className":3449},[671,672],[572,3451,3453,3495],{"className":3452},[676],[572,3454,3456,3467,3475],{"className":3455,"style":2342},[680],[572,3457,3458,3461],{"style":2244},[572,3459],{"className":3460,"style":689},[688],[572,3462,3464],{"className":3463},[635],[572,3465,606],{"className":3466},[635],[572,3468,3469,3472],{"style":706},[572,3470],{"className":3471,"style":689},[688],[572,3473],{"className":3474,"style":714},[713],[572,3476,3477,3480],{"style":2264},[572,3478],{"className":3479,"style":689},[688],[572,3481,3483,3486,3489,3492],{"className":3482},[635],[572,3484,2132],{"className":3485},[1548],[572,3487],{"className":3488,"style":811},[641],[572,3490,606],{"className":3491},[635],[572,3493,1133],{"className":3494},[635,636],[572,3496,737],{"className":3497},[736],[572,3499,3501],{"className":3500},[676],[572,3502,3504],{"className":3503,"style":2283},[680],[572,3505],{},[572,3507],{"className":3508},[750,664],[572,3510],{"className":3511,"style":2316},[641],[572,3513,2140],{"className":3514},[2320],[572,3516],{"className":3517,"style":2316},[641],[572,3519,3521,3524,3586],{"className":3520},[635],[572,3522],{"className":3523},[663,664],[572,3525,3527],{"className":3526},[599],[572,3528,3530,3578],{"className":3529},[671,672],[572,3531,3533,3575],{"className":3532},[676],[572,3534,3536,3547,3555],{"className":3535,"style":2342},[680],[572,3537,3538,3541],{"style":2244},[572,3539],{"className":3540,"style":689},[688],[572,3542,3544],{"className":3543},[635],[572,3545,777],{"className":3546},[635],[572,3548,3549,3552],{"style":706},[572,3550],{"className":3551,"style":689},[688],[572,3553],{"className":3554,"style":714},[713],[572,3556,3557,3560],{"style":2264},[572,3558],{"className":3559,"style":689},[688],[572,3561,3563,3566,3569,3572],{"className":3562},[635],[572,3564,2132],{"className":3565},[1548],[572,3567],{"className":3568,"style":811},[641],[572,3570,777],{"className":3571},[635],[572,3573,1133],{"className":3574},[635,636],[572,3576,737],{"className":3577},[736],[572,3579,3581],{"className":3580},[676],[572,3582,3584],{"className":3583,"style":2283},[680],[572,3585],{},[572,3587],{"className":3588},[750,664],[572,3590],{"className":3591,"style":2316},[641],[572,3593,1475],{"className":3594},[2320],[572,3596],{"className":3597,"style":2316},[641],[572,3599,2176],{"className":3600},[827],[572,3602],{"className":3603,"style":811},[641],[572,3605,3607],{"className":3606,"style":2299},[750,2298],[572,3608,1136],{"className":3609},[2303,695],[564,3611,2499,3612,3731,3732,3760,3761,3859],{},[572,3613,3615,3636],{"className":3614},[575],[572,3616,3618],{"className":3617},[579],[581,3619,3620],{"xmlns":583},[585,3621,3622,3634],{},[588,3623,3624,3626,3628],{},[591,3625,1133],{},[595,3627,597],{},[599,3629,3630,3632],{},[591,3631,609],{},[604,3633,606],{},[614,3635,2524],{"encoding":616},[572,3637,3639,3657],{"className":3638,"ariaHidden":622},[621],[572,3640,3642,3645,3648,3651,3654],{"className":3641},[626],[572,3643],{"className":3644,"style":631},[630],[572,3646,1133],{"className":3647},[635,636],[572,3649],{"className":3650,"style":642},[641],[572,3652,597],{"className":3653},[646],[572,3655],{"className":3656,"style":642},[641],[572,3658,3660,3663],{"className":3659},[626],[572,3661],{"className":3662,"style":2552},[630],[572,3664,3666,3669,3728],{"className":3665},[635],[572,3667],{"className":3668},[663,664],[572,3670,3672],{"className":3671},[599],[572,3673,3675,3720],{"className":3674},[671,672],[572,3676,3678,3717],{"className":3677},[676],[572,3679,3681,3695,3703],{"className":3680,"style":2571},[680],[572,3682,3683,3686],{"style":684},[572,3684],{"className":3685,"style":689},[688],[572,3687,3689],{"className":3688},[693,694,695,696],[572,3690,3692],{"className":3691},[635,696],[572,3693,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ergibt sich wieder die Leibniz-Reihe, mal ",[572,3733,3735,3748],{"className":3734},[575],[572,3736,3738],{"className":3737},[579],[581,3739,3740],{"xmlns":583},[585,3741,3742,3746],{},[588,3743,3744],{},[604,3745,606],{},[614,3747,606],{"encoding":616},[572,3749,3751],{"className":3750,"ariaHidden":622},[621],[572,3752,3754,3757],{"className":3753},[626],[572,3755],{"className":3756,"style":1304},[630],[572,3758,606],{"className":3759},[635],", also ",[572,3762,3764,3782],{"className":3763},[575],[572,3765,3767],{"className":3766},[579],[581,3768,3769],{"xmlns":583},[585,3770,3771,3779],{},[588,3772,3773],{},[599,3774,3775,3777],{},[591,3776,609],{},[604,3778,606],{},[614,3780,3781],{"encoding":616},"\\frac{\\pi}{2}",[572,3783,3785],{"className":3784,"ariaHidden":622},[621],[572,3786,3788,3791],{"className":3787},[626],[572,3789],{"className":3790,"style":2552},[630],[572,3792,3794,3797,3856],{"className":3793},[635],[572,3795],{"className":3796},[663,664],[572,3798,3800],{"className":3799},[599],[572,3801,3803,3848],{"className":3802},[671,672],[572,3804,3806,3845],{"className":3805},[676],[572,3807,3809,3823,3831],{"className":3808,"style":2571},[680],[572,3810,3811,3814],{"style":684},[572,3812],{"className":3813,"style":689},[688],[572,3815,3817],{"className":3816},[693,694,695,696],[572,3818,3820],{"className":3819},[635,696],[572,3821,606],{"className":3822},[635,696],[572,3824,3825,3828],{"style":706},[572,3826],{"className":3827,"style":689},[688],[572,3829],{"className":3830,"style":714},[713],[572,3832,3833,3836],{"style":717},[572,3834],{"className":3835,"style":689},[688],[572,3837,3839],{"className":3838},[693,694,695,696],[572,3840,3842],{"className":3841},[635,696],[572,3843,609],{"className":3844,"style":637},[635,636,696],[572,3846,737],{"className":3847},[736],[572,3849,3851],{"className":3850},[676],[572,3852,3854],{"className":3853,"style":744},[680],[572,3855],{},[572,3857],{"className":3858},[750,664],".",[559,3861,3863],{"id":3862},"typische-fehler","Typische Fehler",[1171,3865,3866,4318,4441,4559],{},[1174,3867,3868,3939,3940,4078,4079,4148,4149,4247,4248,4317],{},[572,3869,3871,3889],{"className":3870},[575],[572,3872,3874],{"className":3873},[579],[581,3875,3876],{"xmlns":583},[585,3877,3878,3886],{},[588,3879,3880],{},[844,3881,3882,3884],{},[591,3883,848],{},[604,3885,851],{},[614,3887,3888],{"encoding":616},"a_0",[572,3890,3892],{"className":3891,"ariaHidden":622},[621],[572,3893,3895,3898],{"className":3894},[626],[572,3896],{"className":3897,"style":1376},[630],[572,3899,3901,3904],{"className":3900},[635],[572,3902,848],{"className":3903},[635,636],[572,3905,3907],{"className":3906},[929],[572,3908,3910,3931],{"className":3909},[671,672],[572,3911,3913,3928],{"className":3912},[676],[572,3914,3917],{"className":3915,"style":3916},[680],"height:0.3011em;",[572,3918,3919,3922],{"style":1267},[572,3920],{"className":3921,"style":1105},[688],[572,3923,3925],{"className":3924},[693,694,695,696],[572,3926,851],{"className":3927},[635,696],[572,3929,737],{"className":3930},[736],[572,3932,3934],{"className":3933},[676],[572,3935,3937],{"className":3936,"style":1286},[680],[572,3938],{}," statt ",[572,3941,3943,3964],{"className":3942},[575],[572,3944,3946],{"className":3945},[579],[581,3947,3948],{"xmlns":583},[585,3949,3950,3962],{},[588,3951,3952],{},[599,3953,3954,3960],{},[844,3955,3956,3958],{},[591,3957,848],{},[604,3959,851],{},[604,3961,606],{},[614,3963,856],{"encoding":616},[572,3965,3967],{"className":3966,"ariaHidden":622},[621],[572,3968,3970,3973],{"className":3969},[626],[572,3971],{"className":3972,"style":866},[630],[572,3974,3976,3979,4075],{"className":3975},[635],[572,3977],{"className":3978},[663,664],[572,3980,3982],{"className":3981},[599],[572,3983,3985,4067],{"className":3984},[671,672],[572,3986,3988,4064],{"className":3987},[676],[572,3989,3991,4005,4013],{"className":3990,"style":885},[680],[572,3992,3993,3996],{"style":684},[572,3994],{"className":3995,"style":689},[688],[572,3997,3999],{"className":3998},[693,694,695,696],[572,4000,4002],{"className":4001},[635,696],[572,4003,606],{"className":4004},[635,696],[572,4006,4007,4010],{"style":706},[572,4008],{"className":4009,"style":689},[688],[572,4011],{"className":4012,"style":714},[713],[572,4014,4015,4018],{"style":910},[572,4016],{"className":4017,"style":689},[688],[572,4019,4021],{"className":4020},[693,694,695,696],[572,4022,4024],{"className":4023},[635,696],[572,4025,4027,4030],{"className":4026},[635,696],[572,4028,848],{"className":4029},[635,636,696],[572,4031,4033],{"className":4032},[929],[572,4034,4036,4056],{"className":4035},[671,672],[572,4037,4039,4053],{"className":4038},[676],[572,4040,4042],{"className":4041,"style":939},[680],[572,4043,4044,4047],{"style":942},[572,4045],{"className":4046,"style":946},[688],[572,4048,4050],{"className":4049},[693,950,951,696],[572,4051,851],{"className":4052},[635,696],[572,4054,737],{"className":4055},[736],[572,4057,4059],{"className":4058},[676],[572,4060,4062],{"className":4061,"style":964},[680],[572,4063],{},[572,4065,737],{"className":4066},[736],[572,4068,4070],{"className":4069},[676],[572,4071,4073],{"className":4072,"style":744},[680],[572,4074],{},[572,4076],{"className":4077},[750,664]," als konstantes Glied schreiben. Mit der üblichen Formel für ",[572,4080,4082,4099],{"className":4081},[575],[572,4083,4085],{"className":4084},[579],[581,4086,4087],{"xmlns":583},[585,4088,4089,4097],{},[588,4090,4091],{},[844,4092,4093,4095],{},[591,4094,848],{},[604,4096,851],{},[614,4098,3888],{"encoding":616},[572,4100,4102],{"className":4101,"ariaHidden":622},[621],[572,4103,4105,4108],{"className":4104},[626],[572,4106],{"className":4107,"style":1376},[630],[572,4109,4111,4114],{"className":4110},[635],[572,4112,848],{"className":4113},[635,636],[572,4115,4117],{"className":4116},[929],[572,4118,4120,4140],{"className":4119},[671,672],[572,4121,4123,4137],{"className":4122},[676],[572,4124,4126],{"className":4125,"style":3916},[680],[572,4127,4128,4131],{"style":1267},[572,4129],{"className":4130,"style":1105},[688],[572,4132,4134],{"className":4133},[693,694,695,696],[572,4135,851],{"className":4136},[635,696],[572,4138,737],{"className":4139},[736],[572,4141,4143],{"className":4142},[676],[572,4144,4146],{"className":4145,"style":1286},[680],[572,4147],{}," gehört der Faktor ",[572,4150,4152,4170],{"className":4151},[575],[572,4153,4155],{"className":4154},[579],[581,4156,4157],{"xmlns":583},[585,4158,4159,4167],{},[588,4160,4161],{},[599,4162,4163,4165],{},[604,4164,1066],{},[604,4166,606],{},[614,4168,4169],{"encoding":616},"\\frac{1}{2}",[572,4171,4173],{"className":4172,"ariaHidden":622},[621],[572,4174,4176,4179],{"className":4175},[626],[572,4177],{"className":4178,"style":656},[630],[572,4180,4182,4185,4244],{"className":4181},[635],[572,4183],{"className":4184},[663,664],[572,4186,4188],{"className":4187},[599],[572,4189,4191,4236],{"className":4190},[671,672],[572,4192,4194,4233],{"className":4193},[676],[572,4195,4197,4211,4219],{"className":4196,"style":681},[680],[572,4198,4199,4202],{"style":684},[572,4200],{"className":4201,"style":689},[688],[572,4203,4205],{"className":4204},[693,694,695,696],[572,4206,4208],{"className":4207},[635,696],[572,4209,606],{"className":4210},[635,696],[572,4212,4213,4216],{"style":706},[572,4214],{"className":4215,"style":689},[688],[572,4217],{"className":4218,"style":714},[713],[572,4220,4221,4224],{"style":717},[572,4222],{"className":4223,"style":689},[688],[572,4225,4227],{"className":4226},[693,694,695,696],[572,4228,4230],{"className":4229},[635,696],[572,4231,1066],{"className":4232},[635,696],[572,4234,737],{"className":4235},[736],[572,4237,4239],{"className":4238},[676],[572,4240,4242],{"className":4241,"style":744},[680],[572,4243],{},[572,4245],{"className":4246},[750,664]," dazu; manche Bücher stecken ihn in die Definition von ",[572,4249,4251,4268],{"className":4250},[575],[572,4252,4254],{"className":4253},[579],[581,4255,4256],{"xmlns":583},[585,4257,4258,4266],{},[588,4259,4260],{},[844,4261,4262,4264],{},[591,4263,848],{},[604,4265,851],{},[614,4267,3888],{"encoding":616},[572,4269,4271],{"className":4270,"ariaHidden":622},[621],[572,4272,4274,4277],{"className":4273},[626],[572,4275],{"className":4276,"style":1376},[630],[572,4278,4280,4283],{"className":4279},[635],[572,4281,848],{"className":4282},[635,636],[572,4284,4286],{"className":4285},[929],[572,4287,4289,4309],{"className":4288},[671,672],[572,4290,4292,4306],{"className":4291},[676],[572,4293,4295],{"className":4294,"style":3916},[680],[572,4296,4297,4300],{"style":1267},[572,4298],{"className":4299,"style":1105},[688],[572,4301,4303],{"className":4302},[693,694,695,696],[572,4304,851],{"className":4305},[635,696],[572,4307,737],{"className":4308},[736],[572,4310,4312],{"className":4311},[676],[572,4313,4315],{"className":4314,"style":1286},[680],[572,4316],{},", dann fehlt er hier.",[1174,4319,4320,4321,4349,4350,4378,4379,4407,4408,3859],{},"An einer Sprungstelle den Funktionswert erwarten. Die Reihe der Rechteckschwingung liefert bei ",[572,4322,4324,4337],{"className":4323},[575],[572,4325,4327],{"className":4326},[579],[581,4328,4329],{"xmlns":583},[585,4330,4331,4335],{},[588,4332,4333],{},[604,4334,851],{},[614,4336,851],{"encoding":616},[572,4338,4340],{"className":4339,"ariaHidden":622},[621],[572,4341,4343,4346],{"className":4342},[626],[572,4344],{"className":4345,"style":1304},[630],[572,4347,851],{"className":4348},[635]," den Wert ",[572,4351,4353,4366],{"className":4352},[575],[572,4354,4356],{"className":4355},[579],[581,4357,4358],{"xmlns":583},[585,4359,4360,4364],{},[588,4361,4362],{},[604,4363,851],{},[614,4365,851],{"encoding":616},[572,4367,4369],{"className":4368,"ariaHidden":622},[621],[572,4370,4372,4375],{"className":4371},[626],[572,4373],{"className":4374,"style":1304},[630],[572,4376,851],{"className":4377},[635],", nicht ",[572,4380,4382,4395],{"className":4381},[575],[572,4383,4385],{"className":4384},[579],[581,4386,4387],{"xmlns":583},[585,4388,4389,4393],{},[588,4390,4391],{},[604,4392,1066],{},[614,4394,1066],{"encoding":616},[572,4396,4398],{"className":4397,"ariaHidden":622},[621],[572,4399,4401,4404],{"className":4400},[626],[572,4402],{"className":4403,"style":1304},[630],[572,4405,1066],{"className":4406},[635]," oder ",[572,4409,4411,4426],{"className":4410},[575],[572,4412,4414],{"className":4413},[579],[581,4415,4416],{"xmlns":583},[585,4417,4418,4424],{},[588,4419,4420,4422],{},[595,4421,1475],{},[604,4423,1066],{},[614,4425,3100],{"encoding":616},[572,4427,4429],{"className":4428,"ariaHidden":622},[621],[572,4430,4432,4435,4438],{"className":4431},[626],[572,4433],{"className":4434,"style":1976},[630],[572,4436,1475],{"className":4437},[635],[572,4439,1066],{"className":4440},[635],[1174,4442,4443,4444,4486,4487,4489,4490,3939,4530,4558],{},"Auf gleichmäßige Konvergenz hoffen. Neben Sprüngen schießen die Teilsummen um etwa ",[572,4445,4447,4467],{"className":4446},[575],[572,4448,4450],{"className":4449},[579],[581,4451,4452],{"xmlns":583},[585,4453,4454,4464],{},[588,4455,4456,4459,4461],{},[604,4457,4458],{},"9",[2178,4460,2180],{},[591,4462,4463],{"mathvariant":1478},"%",[614,4465,4466],{"encoding":616},"9\\,\\%",[572,4468,4470],{"className":4469,"ariaHidden":622},[621],[572,4471,4473,4477,4480,4483],{"className":4472},[626],[572,4474],{"className":4475,"style":4476},[630],"height:0.8056em;vertical-align:-0.0556em;",[572,4478,4458],{"className":4479},[635],[572,4481],{"className":4482,"style":811},[641],[572,4484,4463],{"className":4485},[635]," der Sprunghöhe über (",[568,4488,554],{},"): Bei der Rechteckschwingung erreichen sie etwa ",[572,4491,4493,4508],{"className":4492},[575],[572,4494,4496],{"className":4495},[579],[581,4497,4498],{"xmlns":583},[585,4499,4500,4505],{},[588,4501,4502],{},[604,4503,4504],{},"1,18",[614,4506,4507],{"encoding":616},"1{,}18",[572,4509,4511],{"className":4510,"ariaHidden":622},[621],[572,4512,4514,4517,4520,4526],{"className":4513},[626],[572,4515],{"className":4516,"style":797},[630],[572,4518,1066],{"className":4519},[635],[572,4521,4523],{"className":4522},[635],[572,4524,774],{"className":4525},[807],[572,4527,4529],{"className":4528},[635],"18",[572,4531,4533,4546],{"className":4532},[575],[572,4534,4536],{"className":4535},[579],[581,4537,4538],{"xmlns":583},[585,4539,4540,4544],{},[588,4541,4542],{},[604,4543,1066],{},[614,4545,1066],{"encoding":616},[572,4547,4549],{"className":4548,"ariaHidden":622},[621],[572,4550,4552,4555],{"className":4551},[626],[572,4553],{"className":4554,"style":1304},[630],[572,4556,1066],{"className":4557},[635],", egal wie viele Glieder man nimmt.",[1174,4560,4561,751,4590,4618,4619,2622,4670,4726,4727,3859],{},[572,4562,4564,4578],{"className":4563},[575],[572,4565,4567],{"className":4566},[579],[581,4568,4569],{"xmlns":583},[585,4570,4571,4575],{},[588,4572,4573],{},[591,4574,593],{},[614,4576,4577],{"encoding":616},"\\omega",[572,4579,4581],{"className":4580,"ariaHidden":622},[621],[572,4582,4584,4587],{"className":4583},[626],[572,4585],{"className":4586,"style":631},[630],[572,4588,593],{"className":4589,"style":637},[635,636],[572,4591,4593,4606],{"className":4592},[575],[572,4594,4596],{"className":4595},[579],[581,4597,4598],{"xmlns":583},[585,4599,4600,4604],{},[588,4601,4602],{},[591,4603,612],{},[614,4605,612],{"encoding":616},[572,4607,4609],{"className":4608,"ariaHidden":622},[621],[572,4610,4612,4615],{"className":4611},[626],[572,4613],{"className":4614,"style":1742},[630],[572,4616,612],{"className":4617,"style":703},[635,636]," verwechseln. Bei ",[572,4620,4622,4640],{"className":4621},[575],[572,4623,4625],{"className":4624},[579],[581,4626,4627],{"xmlns":583},[585,4628,4629,4637],{},[588,4630,4631,4633,4635],{},[591,4632,612],{},[595,4634,597],{},[604,4636,1066],{},[614,4638,4639],{"encoding":616},"T = 1",[572,4641,4643,4661],{"className":4642,"ariaHidden":622},[621],[572,4644,4646,4649,4652,4655,4658],{"className":4645},[626],[572,4647],{"className":4648,"style":1742},[630],[572,4650,612],{"className":4651,"style":703},[635,636],[572,4653],{"className":4654,"style":642},[641],[572,4656,597],{"className":4657},[646],[572,4659],{"className":4660,"style":642},[641],[572,4662,4664,4667],{"className":4663},[626],[572,4665],{"className":4666,"style":1304},[630],[572,4668,1066],{"className":4669},[635],[572,4671,4673,4693],{"className":4672},[575],[572,4674,4676],{"className":4675},[579],[581,4677,4678],{"xmlns":583},[585,4679,4680,4690],{},[588,4681,4682,4684,4686,4688],{},[591,4683,593],{},[595,4685,597],{},[604,4687,606],{},[591,4689,609],{},[614,4691,4692],{"encoding":616},"\\omega = 2\\pi",[572,4694,4696,4714],{"className":4695,"ariaHidden":622},[621],[572,4697,4699,4702,4705,4708,4711],{"className":4698},[626],[572,4700],{"className":4701,"style":631},[630],[572,4703,593],{"className":4704,"style":637},[635,636],[572,4706],{"className":4707,"style":642},[641],[572,4709,597],{"className":4710},[646],[572,4712],{"className":4713,"style":642},[641],[572,4715,4717,4720,4723],{"className":4716},[626],[572,4718],{"className":4719,"style":1304},[630],[572,4721,606],{"className":4722},[635],[572,4724,609],{"className":4725,"style":637},[635,636],", die Terme heißen dann ",[572,4728,4730,4759],{"className":4729},[575],[572,4731,4733],{"className":4732},[579],[581,4734,4735],{"xmlns":583},[585,4736,4737,4756],{},[588,4738,4739,4742,4744,4746,4748,4750,4752,4754],{},[591,4740,4741],{},"cos",[595,4743,2135],{},[595,4745,1130],{"stretchy":1129},[604,4747,606],{},[591,4749,609],{},[591,4751,1228],{},[591,4753,1133],{},[595,4755,1136],{"stretchy":1129},[614,4757,4758],{"encoding":616},"\\cos(2\\pi n x)",[572,4760,4762],{"className":4761,"ariaHidden":622},[621],[572,4763,4765,4768,4771,4774,4777,4780,4783,4786],{"className":4764},[626],[572,4766],{"className":4767,"style":1149},[630],[572,4769,4741],{"className":4770},[1548],[572,4772,1130],{"className":4773},[663],[572,4775,606],{"className":4776},[635],[572,4778,609],{"className":4779,"style":637},[635,636],[572,4781,1228],{"className":4782},[635,636],[572,4784,1133],{"className":4785},[635,636],[572,4787,1136],{"className":4788},[750],{"title":4790,"searchDepth":4791,"depth":4791,"links":4792},"",2,[4793,4794,4795],{"id":561,"depth":4791,"text":562},{"id":1702,"depth":4791,"text":1703},{"id":3862,"depth":4791,"text":3863},[4797,4802,4804,4807,4810],{"lhs":4798,"rhs":4799,"where":4800},"sin((2*k - 1)*pi\u002F2)","(-1)^(k + 1)",{"k":4801},3,{"lhs":4803,"rhs":1066},"round(4\u002Fpi*sum((-1).^(0:9999) .\u002F (2*(1:10000) - 1)), 3)",{"lhs":4805,"rhs":4806},"round(sum(map(1:20000, f(n) = 2*(-1)^(n + 1)\u002Fn * sin(n*pi\u002F2))), 3)","round(pi\u002F2, 3)",{"lhs":4808,"rhs":4809},"round(4\u002Fpi*sum(map(1:2000, f(k) = sin((2*k - 1)*pi\u002F4000)\u002F(2*k - 1))), 2)","1.18",{"lhs":4811,"rhs":851},"(1 + (-1))\u002F2","f\\ T\\text{-periodisch, stückweise } C^1,\\ \\omega = \\tfrac{2\\pi}{T}","\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\">stückweise\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>C\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C^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:1.0085em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;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\">1\u003C\u002Fspan>\u003C\u002Fspan>\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>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>\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","fourier-series","f(x) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\bigl( a_n \\cos(n \\omega x) + b_n \\sin(n \\omega x) \\bigr)","\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>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo 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