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Er beträgt ungefähr ",[572,1054,1056,1079],{"className":1055},[575],[572,1057,1059],{"className":1058},[579],[581,1060,1061],{"xmlns":583},[585,1062,1063,1076],{},[588,1064,1065],{},[660,1066,1067,1069],{},[678,1068,714],{},[588,1070,1071,1074],{},[678,1072,1073],{},"12",[641,1075,651],{},[595,1077,1078],{"encoding":597},"\\frac{1}{12n}",[572,1080,1082],{"className":1081,"ariaHidden":603},[602],[572,1083,1085,1089],{"className":1084},[607],[572,1086],{"className":1087,"style":1088},[611],"height:1.1901em;vertical-align:-0.345em;",[572,1090,1092,1095,1161],{"className":1091},[765],[572,1093],{"className":1094},[812,813],[572,1096,1098],{"className":1097},[660],[572,1099,1101,1152],{"className":1100},[736,737],[572,1102,1104,1149],{"className":1103},[741],[572,1105,1108,1126,1134],{"className":1106,"style":1107},[745],"height:0.8451em;",[572,1109,1111,1114],{"style":1110},"top:-2.655em;",[572,1112],{"className":1113,"style":754},[753],[572,1115,1117],{"className":1116},[758,759,760,761],[572,1118,1120,1123],{"className":1119},[765,761],[572,1121,1073],{"className":1122},[765,761],[572,1124,651],{"className":1125},[765,769,761],[572,1127,1128,1131],{"style":957},[572,1129],{"className":1130,"style":754},[753],[572,1132],{"className":1133,"style":965},[964],[572,1135,1137,1140],{"style":1136},"top:-3.394em;",[572,1138],{"className":1139,"style":754},[753],[572,1141,1143],{"className":1142},[758,759,760,761],[572,1144,1146],{"className":1145},[765,761],[572,1147,714],{"className":1148},[765,761],[572,1150,791],{"className":1151},[790],[572,1153,1155],{"className":1154},[741],[572,1156,1159],{"className":1157,"style":1158},[745],"height:0.345em;",[572,1160],{},[572,1162],{"className":1163},[924,813],", die Näherung ist immer etwas zu klein. Mit dem Korrekturfaktor ",[572,1166,1168,1195],{"className":1167},[575],[572,1169,1171],{"className":1170},[579],[581,1172,1173],{"xmlns":583},[585,1174,1175,1192],{},[588,1176,1177,1179,1182],{},[678,1178,714],{},[591,1180,1181],{},"+",[660,1183,1184,1186],{},[678,1185,714],{},[588,1187,1188,1190],{},[678,1189,1073],{},[641,1191,651],{},[595,1193,1194],{"encoding":597},"1 + \\frac{1}{12n}",[572,1196,1198,1219],{"className":1197,"ariaHidden":603},[602],[572,1199,1201,1205,1208,1212,1216],{"className":1200},[607],[572,1202],{"className":1203,"style":1204},[611],"height:0.7278em;vertical-align:-0.0833em;",[572,1206,714],{"className":1207},[765],[572,1209],{"className":1210,"style":1211},[804],"margin-right:0.2222em;",[572,1213,1181],{"className":1214},[1215],"mbin",[572,1217],{"className":1218,"style":1211},[804],[572,1220,1222,1225],{"className":1221},[607],[572,1223],{"className":1224,"style":1088},[611],[572,1226,1228,1231,1293],{"className":1227},[765],[572,1229],{"className":1230},[812,813],[572,1232,1234],{"className":1233},[660],[572,1235,1237,1285],{"className":1236},[736,737],[572,1238,1240,1282],{"className":1239},[741],[572,1241,1243,1260,1268],{"className":1242,"style":1107},[745],[572,1244,1245,1248],{"style":1110},[572,1246],{"className":1247,"style":754},[753],[572,1249,1251],{"className":1250},[758,759,760,761],[572,1252,1254,1257],{"className":1253},[765,761],[572,1255,1073],{"className":1256},[765,761],[572,1258,651],{"className":1259},[765,769,761],[572,1261,1262,1265],{"style":957},[572,1263],{"className":1264,"style":754},[753],[572,1266],{"className":1267,"style":965},[964],[572,1269,1270,1273],{"style":1136},[572,1271],{"className":1272,"style":754},[753],[572,1274,1276],{"className":1275},[758,759,760,761],[572,1277,1279],{"className":1278},[765,761],[572,1280,714],{"className":1281},[765,761],[572,1283,791],{"className":1284},[790],[572,1286,1288],{"className":1287},[741],[572,1289,1291],{"className":1290,"style":1158},[745],[572,1292],{},[572,1294],{"className":1295},[924,813]," wird sie deutlich genauer.",[564,1298,1299,1300,1537,1538,1645],{},"Logarithmiert erhält man ",[572,1301,1303,1362],{"className":1302},[575],[572,1304,1306],{"className":1305},[579],[581,1307,1308],{"xmlns":583},[585,1309,1310,1359],{},[588,1311,1312,1315,1317,1319,1321,1324,1326,1328,1330,1332,1335,1337,1339,1345,1347,1349,1351,1353,1355,1357],{},[641,1313,1314],{},"ln",[591,1316,646],{},[641,1318,651],{},[591,1320,669],{"stretchy":668},[591,1322,1323],{},"≈",[641,1325,651],{},[641,1327,1314],{},[591,1329,646],{},[641,1331,651],{},[591,1333,1334],{},"−",[641,1336,651],{},[591,1338,1181],{},[660,1340,1341,1343],{},[678,1342,714],{},[678,1344,680],{},[641,1346,1314],{},[591,1348,646],{},[591,1350,692],{"stretchy":668},[678,1352,680],{},[641,1354,683],{},[641,1356,651],{},[591,1358,706],{"stretchy":668},[595,1360,1361],{"encoding":597},"\\ln n! \\approx n \\ln n - n + \\frac{1}{2}\\ln(2\\pi n)",[572,1363,1365,1392,1423,1442],{"className":1364,"ariaHidden":603},[602],[572,1366,1368,1371,1374,1377,1380,1383,1386,1389],{"className":1367},[607],[572,1369],{"className":1370,"style":746},[611],[572,1372,1314],{"className":1373},[731],[572,1375],{"className":1376,"style":805},[804],[572,1378,651],{"className":1379},[765,769],[572,1381,669],{"className":1382},[924],[572,1384],{"className":1385,"style":999},[804],[572,1387,1323],{"className":1388},[616],[572,1390],{"className":1391,"style":999},[804],[572,1393,1395,1399,1402,1405,1408,1411,1414,1417,1420],{"className":1394},[607],[572,1396],{"className":1397,"style":1398},[611],"height:0.7778em;vertical-align:-0.0833em;",[572,1400,651],{"className":1401},[765,769],[572,1403],{"className":1404,"style":805},[804],[572,1406,1314],{"className":1407},[731],[572,1409],{"className":1410,"style":805},[804],[572,1412,651],{"className":1413},[765,769],[572,1415],{"className":1416,"style":1211},[804],[572,1418,1334],{"className":1419},[1215],[572,1421],{"className":1422,"style":1211},[804],[572,1424,1426,1430,1433,1436,1439],{"className":1425},[607],[572,1427],{"className":1428,"style":1429},[611],"height:0.6667em;vertical-align:-0.0833em;",[572,1431,651],{"className":1432},[765,769],[572,1434],{"className":1435,"style":1211},[804],[572,1437,1181],{"className":1438},[1215],[572,1440],{"className":1441,"style":1211},[804],[572,1443,1445,1448,1516,1519,1522,1525,1528,1531,1534],{"className":1444},[607],[572,1446],{"className":1447,"style":1088},[611],[572,1449,1451,1454,1513],{"className":1450},[765],[572,1452],{"className":1453},[812,813],[572,1455,1457],{"className":1456},[660],[572,1458,1460,1505],{"className":1459},[736,737],[572,1461,1463,1502],{"className":1462},[741],[572,1464,1466,1480,1488],{"className":1465,"style":1107},[745],[572,1467,1468,1471],{"style":1110},[572,1469],{"className":1470,"style":754},[753],[572,1472,1474],{"className":1473},[758,759,760,761],[572,1475,1477],{"className":1476},[765,761],[572,1478,680],{"className":1479},[765,761],[572,1481,1482,1485],{"style":957},[572,1483],{"className":1484,"style":754},[753],[572,1486],{"className":1487,"style":965},[964],[572,1489,1490,1493],{"style":1136},[572,1491],{"className":1492,"style":754},[753],[572,1494,1496],{"className":1495},[758,759,760,761],[572,1497,1499],{"className":1498},[765,761],[572,1500,714],{"className":1501},[765,761],[572,1503,791],{"className":1504},[790],[572,1506,1508],{"className":1507},[741],[572,1509,1511],{"className":1510,"style":1158},[745],[572,1512],{},[572,1514],{"className":1515},[924,813],[572,1517],{"className":1518,"style":805},[804],[572,1520,1314],{"className":1521},[731],[572,1523,692],{"className":1524},[812],[572,1526,680],{"className":1527},[765],[572,1529,683],{"className":1530,"style":867},[765,769],[572,1532,651],{"className":1533},[765,769],[572,1535,706],{"className":1536},[924],". Die grobe Form ",[572,1539,1541,1575],{"className":1540},[575],[572,1542,1544],{"className":1543},[579],[581,1545,1546],{"xmlns":583},[585,1547,1548,1572],{},[588,1549,1550,1552,1554,1556,1558,1560,1562,1564,1566,1568,1570],{},[641,1551,1314],{},[591,1553,646],{},[641,1555,651],{},[591,1557,669],{"stretchy":668},[591,1559,1323],{},[641,1561,651],{},[641,1563,1314],{},[591,1565,646],{},[641,1567,651],{},[591,1569,1334],{},[641,1571,651],{},[595,1573,1574],{"encoding":597},"\\ln n! \\approx n \\ln n - n",[572,1576,1578,1605,1635],{"className":1577,"ariaHidden":603},[602],[572,1579,1581,1584,1587,1590,1593,1596,1599,1602],{"className":1580},[607],[572,1582],{"className":1583,"style":746},[611],[572,1585,1314],{"className":1586},[731],[572,1588],{"className":1589,"style":805},[804],[572,1591,651],{"className":1592},[765,769],[572,1594,669],{"className":1595},[924],[572,1597],{"className":1598,"style":999},[804],[572,1600,1323],{"className":1601},[616],[572,1603],{"className":1604,"style":999},[804],[572,1606,1608,1611,1614,1617,1620,1623,1626,1629,1632],{"className":1607},[607],[572,1609],{"className":1610,"style":1398},[611],[572,1612,651],{"className":1613},[765,769],[572,1615],{"className":1616,"style":805},[804],[572,1618,1314],{"className":1619},[731],[572,1621],{"className":1622,"style":805},[804],[572,1624,651],{"className":1625},[765,769],[572,1627],{"className":1628,"style":1211},[804],[572,1630,1334],{"className":1631},[1215],[572,1633],{"className":1634,"style":1211},[804],[572,1636,1638,1642],{"className":1637},[607],[572,1639],{"className":1640,"style":1641},[611],"height:0.4306em;",[572,1643,651],{"className":1644},[765,769]," genügt oft in der Statistik und der statistischen Physik, wenn es nur auf die Größenordnung ankommt.",[564,1647,1648,1649,1677],{},"Die Formel ist nützlich, um Grenzwerte mit Fakultäten zu bestimmen, Binomialkoeffizienten für große ",[572,1650,1652,1665],{"className":1651},[575],[572,1653,1655],{"className":1654},[579],[581,1656,1657],{"xmlns":583},[585,1658,1659,1663],{},[588,1660,1661],{},[641,1662,651],{},[595,1664,651],{"encoding":597},[572,1666,1668],{"className":1667,"ariaHidden":603},[602],[572,1669,1671,1674],{"className":1670},[607],[572,1672],{"className":1673,"style":1641},[611],[572,1675,651],{"className":1676},[765,769]," abzuschätzen und Fakultäten zu berechnen, die den Taschenrechner überfordern.",[559,1679,1681],{"id":1680},"beispiele","Beispiele",[564,1683,1684,1685,1737,1738,1817],{},"Für ",[572,1686,1688,1707],{"className":1687},[575],[572,1689,1691],{"className":1690},[579],[581,1692,1693],{"xmlns":583},[585,1694,1695,1704],{},[588,1696,1697,1699,1701],{},[641,1698,651],{},[591,1700,711],{},[678,1702,1703],{},"10",[595,1705,1706],{"encoding":597},"n = 10",[572,1708,1710,1728],{"className":1709,"ariaHidden":603},[602],[572,1711,1713,1716,1719,1722,1725],{"className":1712},[607],[572,1714],{"className":1715,"style":1641},[611],[572,1717,651],{"className":1718},[765,769],[572,1720],{"className":1721,"style":999},[804],[572,1723,711],{"className":1724},[616],[572,1726],{"className":1727,"style":999},[804],[572,1729,1731,1734],{"className":1730},[607],[572,1732],{"className":1733,"style":1012},[611],[572,1735,1703],{"className":1736},[765]," ist ",[572,1739,1741,1772],{"className":1740},[575],[572,1742,1744],{"className":1743},[579],[581,1745,1746],{"xmlns":583},[585,1747,1748,1769],{},[588,1749,1750,1752,1754,1756,1759,1761,1764,1766],{},[678,1751,1703],{},[591,1753,669],{"stretchy":668},[591,1755,711],{},[678,1757,1758],{},"3",[687,1760,689],{},[678,1762,1763],{},"628",[687,1765,689],{},[678,1767,1768],{},"800",[595,1770,1771],{"encoding":597},"10! = 3\\,628\\,800",[572,1773,1775,1796],{"className":1774,"ariaHidden":603},[602],[572,1776,1778,1781,1784,1787,1790,1793],{"className":1777},[607],[572,1779],{"className":1780,"style":746},[611],[572,1782,1703],{"className":1783},[765],[572,1785,669],{"className":1786},[924],[572,1788],{"className":1789,"style":999},[804],[572,1791,711],{"className":1792},[616],[572,1794],{"className":1795,"style":999},[804],[572,1797,1799,1802,1805,1808,1811,1814],{"className":1798},[607],[572,1800],{"className":1801,"style":1012},[611],[572,1803,1758],{"className":1804},[765],[572,1806],{"className":1807,"style":805},[804],[572,1809,1763],{"className":1810},[765],[572,1812],{"className":1813,"style":805},[804],[572,1815,1768],{"className":1816},[765],". Stirling liefert",[572,1819,1821],{"className":1820},[621],[572,1822,1824,1878],{"className":1823},[575],[572,1825,1827],{"className":1826},[579],[581,1828,1829],{"xmlns":583,"display":630},[585,1830,1831,1875],{},[588,1832,1833,1842,1845,1861,1863,1865,1867,1870,1872],{},[673,1834,1835],{},[588,1836,1837,1840],{},[678,1838,1839],{},"20",[641,1841,683],{},[591,1843,1844],{},"⋅",[702,1846,1847,1859],{},[588,1848,1849,1851,1857],{},[591,1850,692],{"fence":603},[660,1852,1853,1855],{},[678,1854,1703],{},[641,1856,700],{},[591,1858,706],{"fence":603},[678,1860,1703],{},[591,1862,1323],{},[678,1864,1758],{},[687,1866,689],{},[678,1868,1869],{},"598",[687,1871,689],{},[678,1873,1874],{},"696",[595,1876,1877],{"encoding":597},"\\sqrt{20\\pi} \\cdot \\left(\\frac{10}{e}\\right)^{10} \\approx 3\\,598\\,696",[572,1879,1881,1950,2081],{"className":1880,"ariaHidden":603},[602],[572,1882,1884,1888,1941,1944,1947],{"className":1883},[607],[572,1885],{"className":1886,"style":1887},[611],"height:1.04em;vertical-align:-0.0839em;",[572,1889,1891],{"className":1890},[765,839],[572,1892,1894,1932],{"className":1893},[736,737],[572,1895,1897,1929],{"className":1896},[741],[572,1898,1901,1916],{"className":1899,"style":1900},[745],"height:0.9561em;",[572,1902,1904,1907],{"className":1903,"style":778},[853],[572,1905],{"className":1906,"style":754},[753],[572,1908,1910,1913],{"className":1909,"style":860},[765],[572,1911,1839],{"className":1912},[765],[572,1914,683],{"className":1915,"style":867},[765,769],[572,1917,1919,1922],{"style":1918},"top:-2.9161em;",[572,1920],{"className":1921,"style":754},[753],[572,1923,1925],{"className":1924,"style":881},[880],[883,1926,1927],{"xmlns":885,"width":886,"height":887,"viewBox":888,"preserveAspectRatio":889},[891,1928],{"d":893},[572,1930,791],{"className":1931},[790],[572,1933,1935],{"className":1934},[741],[572,1936,1939],{"className":1937,"style":1938},[745],"height:0.0839em;",[572,1940],{},[572,1942],{"className":1943,"style":1211},[804],[572,1945,1844],{"className":1946},[1215],[572,1948],{"className":1949,"style":1211},[804],[572,1951,1953,1957,2072,2075,2078],{"className":1952},[607],[572,1954],{"className":1955,"style":1956},[611],"height:2.604em;vertical-align:-0.95em;",[572,1958,1961,2044],{"className":1959},[1960],"minner",[572,1962,1964,1973,2038],{"className":1963},[1960],[572,1965,1969],{"className":1966,"style":1968},[812,1967],"delimcenter","top:0em;",[572,1970,692],{"className":1971},[1972,760],"delimsizing",[572,1974,1976,1979,2035],{"className":1975},[765],[572,1977],{"className":1978},[812,813],[572,1980,1982],{"className":1981},[660],[572,1983,1985,2026],{"className":1984},[736,737],[572,1986,1988,2023],{"className":1987},[741],[572,1989,1992,2004,2012],{"className":1990,"style":1991},[745],"height:1.3214em;",[572,1993,1995,1998],{"style":1994},"top:-2.314em;",[572,1996],{"className":1997,"style":754},[753],[572,1999,2001],{"className":2000},[765],[572,2002,700],{"className":2003},[765,769],[572,2005,2006,2009],{"style":957},[572,2007],{"className":2008,"style":754},[753],[572,2010],{"className":2011,"style":965},[964],[572,2013,2014,2017],{"style":968},[572,2015],{"className":2016,"style":754},[753],[572,2018,2020],{"className":2019},[765],[572,2021,1703],{"className":2022},[765],[572,2024,791],{"className":2025},[790],[572,2027,2029],{"className":2028},[741],[572,2030,2033],{"className":2031,"style":2032},[745],"height:0.686em;",[572,2034],{},[572,2036],{"className":2037},[924,813],[572,2039,2041],{"className":2040,"style":1968},[924,1967],[572,2042,706],{"className":2043},[1972,760],[572,2045,2047],{"className":2046},[931],[572,2048,2050],{"className":2049},[736],[572,2051,2053],{"className":2052},[741],[572,2054,2057],{"className":2055,"style":2056},[745],"height:1.654em;",[572,2058,2060,2063],{"style":2059},"top:-3.9029em;margin-right:0.05em;",[572,2061],{"className":2062,"style":948},[753],[572,2064,2066],{"className":2065},[758,759,760,761],[572,2067,2069],{"className":2068},[765,761],[572,2070,1703],{"className":2071},[765,761],[572,2073],{"className":2074,"style":999},[804],[572,2076,1323],{"className":2077},[616],[572,2079],{"className":2080,"style":999},[804],[572,2082,2084,2087,2090,2093,2096,2099],{"className":2083},[607],[572,2085],{"className":2086,"style":1012},[611],[572,2088,1758],{"className":2089},[765],[572,2091],{"className":2092,"style":805},[804],[572,2094,1869],{"className":2095},[765],[572,2097],{"className":2098,"style":805},[804],[572,2100,1874],{"className":2101},[765],[564,2103,2104,2105,2159,2160,2259,2260,2380,2381,2431,2432,2461],{},"Der relative Fehler ist etwa ",[572,2106,2108,2128],{"className":2107},[575],[572,2109,2111],{"className":2110},[579],[581,2112,2113],{"xmlns":583},[585,2114,2115,2125],{},[588,2116,2117,2120,2122],{},[678,2118,2119],{},"0,84",[687,2121,689],{},[641,2123,2124],{"mathvariant":657},"%",[595,2126,2127],{"encoding":597},"0{,}84\\,\\%",[572,2129,2131],{"className":2130,"ariaHidden":603},[602],[572,2132,2134,2138,2141,2149,2153,2156],{"className":2133},[607],[572,2135],{"className":2136,"style":2137},[611],"height:0.9444em;vertical-align:-0.1944em;",[572,2139,1037],{"className":2140},[765],[572,2142,2144],{"className":2143},[765],[572,2145,2148],{"className":2146},[2147],"mpunct",",",[572,2150,2152],{"className":2151},[765],"84",[572,2154],{"className":2155,"style":805},[804],[572,2157,2124],{"className":2158},[765],", also nahe bei ",[572,2161,2163,2182],{"className":2162},[575],[572,2164,2166],{"className":2165},[579],[581,2167,2168],{"xmlns":583},[585,2169,2170,2179],{},[588,2171,2172],{},[660,2173,2174,2176],{},[678,2175,714],{},[678,2177,2178],{},"120",[595,2180,2181],{"encoding":597},"\\frac{1}{120}",[572,2183,2185],{"className":2184,"ariaHidden":603},[602],[572,2186,2188,2191],{"className":2187},[607],[572,2189],{"className":2190,"style":1088},[611],[572,2192,2194,2197,2256],{"className":2193},[765],[572,2195],{"className":2196},[812,813],[572,2198,2200],{"className":2199},[660],[572,2201,2203,2248],{"className":2202},[736,737],[572,2204,2206,2245],{"className":2205},[741],[572,2207,2209,2223,2231],{"className":2208,"style":1107},[745],[572,2210,2211,2214],{"style":1110},[572,2212],{"className":2213,"style":754},[753],[572,2215,2217],{"className":2216},[758,759,760,761],[572,2218,2220],{"className":2219},[765,761],[572,2221,2178],{"className":2222},[765,761],[572,2224,2225,2228],{"style":957},[572,2226],{"className":2227,"style":754},[753],[572,2229],{"className":2230,"style":965},[964],[572,2232,2233,2236],{"style":1136},[572,2234],{"className":2235,"style":754},[753],[572,2237,2239],{"className":2238},[758,759,760,761],[572,2240,2242],{"className":2241},[765,761],[572,2243,714],{"className":2244},[765,761],[572,2246,791],{"className":2247},[790],[572,2249,2251],{"className":2250},[741],[572,2252,2254],{"className":2253,"style":1158},[745],[572,2255],{},[572,2257],{"className":2258},[924,813],". Mit dem Korrekturfaktor ",[572,2261,2263,2285],{"className":2262},[575],[572,2264,2266],{"className":2265},[579],[581,2267,2268],{"xmlns":583},[585,2269,2270,2282],{},[588,2271,2272,2274,2276],{},[678,2273,714],{},[591,2275,1181],{},[660,2277,2278,2280],{},[678,2279,714],{},[678,2281,2178],{},[595,2283,2284],{"encoding":597},"1 + \\frac{1}{120}",[572,2286,2288,2306],{"className":2287,"ariaHidden":603},[602],[572,2289,2291,2294,2297,2300,2303],{"className":2290},[607],[572,2292],{"className":2293,"style":1204},[611],[572,2295,714],{"className":2296},[765],[572,2298],{"className":2299,"style":1211},[804],[572,2301,1181],{"className":2302},[1215],[572,2304],{"className":2305,"style":1211},[804],[572,2307,2309,2312],{"className":2308},[607],[572,2310],{"className":2311,"style":1088},[611],[572,2313,2315,2318,2377],{"className":2314},[765],[572,2316],{"className":2317},[812,813],[572,2319,2321],{"className":2320},[660],[572,2322,2324,2369],{"className":2323},[736,737],[572,2325,2327,2366],{"className":2326},[741],[572,2328,2330,2344,2352],{"className":2329,"style":1107},[745],[572,2331,2332,2335],{"style":1110},[572,2333],{"className":2334,"style":754},[753],[572,2336,2338],{"className":2337},[758,759,760,761],[572,2339,2341],{"className":2340},[765,761],[572,2342,2178],{"className":2343},[765,761],[572,2345,2346,2349],{"style":957},[572,2347],{"className":2348,"style":754},[753],[572,2350],{"className":2351,"style":965},[964],[572,2353,2354,2357],{"style":1136},[572,2355],{"className":2356,"style":754},[753],[572,2358,2360],{"className":2359},[758,759,760,761],[572,2361,2363],{"className":2362},[765,761],[572,2364,714],{"className":2365},[765,761],[572,2367,791],{"className":2368},[790],[572,2370,2372],{"className":2371},[741],[572,2373,2375],{"className":2374,"style":1158},[745],[572,2376],{},[572,2378],{"className":2379},[924,813]," ergibt sich ",[572,2382,2384,2407],{"className":2383},[575],[572,2385,2387],{"className":2386},[579],[581,2388,2389],{"xmlns":583},[585,2390,2391,2404],{},[588,2392,2393,2395,2397,2399,2401],{},[678,2394,1758],{},[687,2396,689],{},[678,2398,1763],{},[687,2400,689],{},[678,2402,2403],{},"685",[595,2405,2406],{"encoding":597},"3\\,628\\,685",[572,2408,2410],{"className":2409,"ariaHidden":603},[602],[572,2411,2413,2416,2419,2422,2425,2428],{"className":2412},[607],[572,2414],{"className":2415,"style":1012},[611],[572,2417,1758],{"className":2418},[765],[572,2420],{"className":2421,"style":805},[804],[572,2423,1763],{"className":2424},[765],[572,2426],{"className":2427,"style":805},[804],[572,2429,2403],{"className":2430},[765],", nur noch ",[572,2433,2435,2449],{"className":2434},[575],[572,2436,2438],{"className":2437},[579],[581,2439,2440],{"xmlns":583},[585,2441,2442,2447],{},[588,2443,2444],{},[678,2445,2446],{},"115",[595,2448,2446],{"encoding":597},[572,2450,2452],{"className":2451,"ariaHidden":603},[602],[572,2453,2455,2458],{"className":2454},[607],[572,2456],{"className":2457,"style":1012},[611],[572,2459,2446],{"className":2460},[765]," daneben.",[564,2463,2464,2465,2500,2501,2529],{},"Wie viele Stellen hat ",[572,2466,2468,2485],{"className":2467},[575],[572,2469,2471],{"className":2470},[579],[581,2472,2473],{"xmlns":583},[585,2474,2475,2482],{},[588,2476,2477,2480],{},[678,2478,2479],{},"100",[591,2481,669],{"stretchy":668},[595,2483,2484],{"encoding":597},"100!",[572,2486,2488],{"className":2487,"ariaHidden":603},[602],[572,2489,2491,2494,2497],{"className":2490},[607],[572,2492],{"className":2493,"style":746},[611],[572,2495,2479],{"className":2496},[765],[572,2498,669],{"className":2499},[924],"? Logarithmiert zur Basis ",[572,2502,2504,2517],{"className":2503},[575],[572,2505,2507],{"className":2506},[579],[581,2508,2509],{"xmlns":583},[585,2510,2511,2515],{},[588,2512,2513],{},[678,2514,1703],{},[595,2516,1703],{"encoding":597},[572,2518,2520],{"className":2519,"ariaHidden":603},[602],[572,2521,2523,2526],{"className":2522},[607],[572,2524],{"className":2525,"style":1012},[611],[572,2527,1703],{"className":2528},[765],":",[572,2531,2533],{"className":2532},[621],[572,2534,2536,2593],{"className":2535},[575],[572,2537,2539],{"className":2538},[579],[581,2540,2541],{"xmlns":583,"display":630},[585,2542,2543,2590],{},[588,2544,2545,2548,2550,2552,2554,2556,2558,2560,2569,2571,2573,2575,2577,2579,2585,2587],{},[641,2546,2547],{},"lg",[591,2549,646],{},[678,2551,2479],{},[591,2553,669],{"stretchy":668},[591,2555,1323],{},[641,2557,2547],{},[591,2559,646],{},[673,2561,2562],{},[588,2563,2564,2567],{},[678,2565,2566],{},"200",[641,2568,683],{},[591,2570,1181],{},[678,2572,2479],{},[591,2574,1844],{},[641,2576,2547],{},[591,2578,646],{},[660,2580,2581,2583],{},[678,2582,2479],{},[641,2584,700],{},[591,2586,1323],{},[678,2588,2589],{},"157,97",[595,2591,2592],{"encoding":597},"\\lg 100! \\approx \\lg\\sqrt{200\\pi} + 100 \\cdot \\lg\\frac{100}{e} \\approx 157{,}97",[572,2594,2596,2629,2703,2721,2807],{"className":2595,"ariaHidden":603},[602],[572,2597,2599,2603,2611,2614,2617,2620,2623,2626],{"className":2598},[607],[572,2600],{"className":2601,"style":2602},[611],"height:0.8889em;vertical-align:-0.1944em;",[572,2604,2606,2607],{"className":2605},[731],"l",[572,2608,2610],{"style":2609},"margin-right:0.0139em;","g",[572,2612],{"className":2613,"style":805},[804],[572,2615,2479],{"className":2616},[765],[572,2618,669],{"className":2619},[924],[572,2621],{"className":2622,"style":999},[804],[572,2624,1323],{"className":2625},[616],[572,2627],{"className":2628,"style":999},[804],[572,2630,2632,2636,2641,2644,2694,2697,2700],{"className":2631},[607],[572,2633],{"className":2634,"style":2635},[611],"height:1.1505em;vertical-align:-0.1944em;",[572,2637,2606,2639],{"className":2638},[731],[572,2640,2610],{"style":2609},[572,2642],{"className":2643,"style":805},[804],[572,2645,2647],{"className":2646},[765,839],[572,2648,2650,2686],{"className":2649},[736,737],[572,2651,2653,2683],{"className":2652},[741],[572,2654,2656,2671],{"className":2655,"style":1900},[745],[572,2657,2659,2662],{"className":2658,"style":778},[853],[572,2660],{"className":2661,"style":754},[753],[572,2663,2665,2668],{"className":2664,"style":860},[765],[572,2666,2566],{"className":2667},[765],[572,2669,683],{"className":2670,"style":867},[765,769],[572,2672,2673,2676],{"style":1918},[572,2674],{"className":2675,"style":754},[753],[572,2677,2679],{"className":2678,"style":881},[880],[883,2680,2681],{"xmlns":885,"width":886,"height":887,"viewBox":888,"preserveAspectRatio":889},[891,2682],{"d":893},[572,2684,791],{"className":2685},[790],[572,2687,2689],{"className":2688},[741],[572,2690,2692],{"className":2691,"style":1938},[745],[572,2693],{},[572,2695],{"className":2696,"style":1211},[804],[572,2698,1181],{"className":2699},[1215],[572,2701],{"className":2702,"style":1211},[804],[572,2704,2706,2709,2712,2715,2718],{"className":2705},[607],[572,2707],{"className":2708,"style":1012},[611],[572,2710,2479],{"className":2711},[765],[572,2713],{"className":2714,"style":1211},[804],[572,2716,1844],{"className":2717},[1215],[572,2719],{"className":2720,"style":1211},[804],[572,2722,2724,2728,2733,2736,2798,2801,2804],{"className":2723},[607],[572,2725],{"className":2726,"style":2727},[611],"height:2.0074em;vertical-align:-0.686em;",[572,2729,2606,2731],{"className":2730},[731],[572,2732,2610],{"style":2609},[572,2734],{"className":2735,"style":805},[804],[572,2737,2739,2742,2795],{"className":2738},[765],[572,2740],{"className":2741},[812,813],[572,2743,2745],{"className":2744},[660],[572,2746,2748,2787],{"className":2747},[736,737],[572,2749,2751,2784],{"className":2750},[741],[572,2752,2754,2765,2773],{"className":2753,"style":1991},[745],[572,2755,2756,2759],{"style":1994},[572,2757],{"className":2758,"style":754},[753],[572,2760,2762],{"className":2761},[765],[572,2763,700],{"className":2764},[765,769],[572,2766,2767,2770],{"style":957},[572,2768],{"className":2769,"style":754},[753],[572,2771],{"className":2772,"style":965},[964],[572,2774,2775,2778],{"style":968},[572,2776],{"className":2777,"style":754},[753],[572,2779,2781],{"className":2780},[765],[572,2782,2479],{"className":2783},[765],[572,2785,791],{"className":2786},[790],[572,2788,2790],{"className":2789},[741],[572,2791,2793],{"className":2792,"style":2032},[745],[572,2794],{},[572,2796],{"className":2797},[924,813],[572,2799],{"className":2800,"style":999},[804],[572,2802,1323],{"className":2803},[616],[572,2805],{"className":2806,"style":999},[804],[572,2808,2810,2814,2818,2824],{"className":2809},[607],[572,2811],{"className":2812,"style":2813},[611],"height:0.8389em;vertical-align:-0.1944em;",[572,2815,2817],{"className":2816},[765],"157",[572,2819,2821],{"className":2820},[765],[572,2822,2148],{"className":2823},[2147],[572,2825,2827],{"className":2826},[765],"97",[564,2829,2830,2831,2864,2865,2894],{},"Also hat ",[572,2832,2834,2849],{"className":2833},[575],[572,2835,2837],{"className":2836},[579],[581,2838,2839],{"xmlns":583},[585,2840,2841,2847],{},[588,2842,2843,2845],{},[678,2844,2479],{},[591,2846,669],{"stretchy":668},[595,2848,2484],{"encoding":597},[572,2850,2852],{"className":2851,"ariaHidden":603},[602],[572,2853,2855,2858,2861],{"className":2854},[607],[572,2856],{"className":2857,"style":746},[611],[572,2859,2479],{"className":2860},[765],[572,2862,669],{"className":2863},[924]," genau ",[572,2866,2868,2882],{"className":2867},[575],[572,2869,2871],{"className":2870},[579],[581,2872,2873],{"xmlns":583},[585,2874,2875,2880],{},[588,2876,2877],{},[678,2878,2879],{},"158",[595,2881,2879],{"encoding":597},[572,2883,2885],{"className":2884,"ariaHidden":603},[602],[572,2886,2888,2891],{"className":2887},[607],[572,2889],{"className":2890,"style":1012},[611],[572,2892,2879],{"className":2893},[765]," Stellen.",[559,2896,2898],{"id":2897},"typische-fehler","Typische Fehler",[2900,2901,2902,3055,3316],"ul",{},[2903,2904,2905,2906,2934,2935,2986,2987,2461],"li",{},"Kleinen absoluten Fehler erwarten. Der Quotient geht gegen ",[572,2907,2909,2922],{"className":2908},[575],[572,2910,2912],{"className":2911},[579],[581,2913,2914],{"xmlns":583},[585,2915,2916,2920],{},[588,2917,2918],{},[678,2919,714],{},[595,2921,714],{"encoding":597},[572,2923,2925],{"className":2924,"ariaHidden":603},[602],[572,2926,2928,2931],{"className":2927},[607],[572,2929],{"className":2930,"style":1012},[611],[572,2932,714],{"className":2933},[765],", die Differenz wächst aber: Bei ",[572,2936,2938,2956],{"className":2937},[575],[572,2939,2941],{"className":2940},[579],[581,2942,2943],{"xmlns":583},[585,2944,2945,2953],{},[588,2946,2947,2949,2951],{},[641,2948,651],{},[591,2950,711],{},[678,2952,1839],{},[595,2954,2955],{"encoding":597},"n = 20",[572,2957,2959,2977],{"className":2958,"ariaHidden":603},[602],[572,2960,2962,2965,2968,2971,2974],{"className":2961},[607],[572,2963],{"className":2964,"style":1641},[611],[572,2966,651],{"className":2967},[765,769],[572,2969],{"className":2970,"style":999},[804],[572,2972,711],{"className":2973},[616],[572,2975],{"className":2976,"style":999},[804],[572,2978,2980,2983],{"className":2979},[607],[572,2981],{"className":2982,"style":1012},[611],[572,2984,1839],{"className":2985},[765]," liegt die Näherung um etwa ",[572,2988,2990,3009],{"className":2989},[575],[572,2991,2993],{"className":2992},[579],[581,2994,2995],{"xmlns":583},[585,2996,2997,3006],{},[588,2998,2999],{},[702,3000,3001,3003],{},[678,3002,1703],{},[678,3004,3005],{},"16",[595,3007,3008],{"encoding":597},"10^{16}",[572,3010,3012],{"className":3011,"ariaHidden":603},[602],[572,3013,3015,3019,3022],{"className":3014},[607],[572,3016],{"className":3017,"style":3018},[611],"height:0.8141em;",[572,3020,714],{"className":3021},[765],[572,3023,3025,3028],{"className":3024},[765],[572,3026,1037],{"className":3027},[765],[572,3029,3031],{"className":3030},[931],[572,3032,3034],{"className":3033},[736],[572,3035,3037],{"className":3036},[741],[572,3038,3040],{"className":3039,"style":3018},[745],[572,3041,3043,3046],{"style":3042},"top:-3.063em;margin-right:0.05em;",[572,3044],{"className":3045,"style":948},[753],[572,3047,3049],{"className":3048},[758,759,760,761],[572,3050,3052],{"className":3051},[765,761],[572,3053,3005],{"className":3054},[765,761],[2903,3056,3057,3058,3146,3147,3228,3229,3315],{},"Den Faktor ",[572,3059,3061,3083],{"className":3060},[575],[572,3062,3064],{"className":3063},[579],[581,3065,3066],{"xmlns":583},[585,3067,3068,3080],{},[588,3069,3070],{},[673,3071,3072],{},[588,3073,3074,3076,3078],{},[678,3075,680],{},[641,3077,683],{},[641,3079,651],{},[595,3081,3082],{"encoding":597},"\\sqrt{2\\pi n}",[572,3084,3086],{"className":3085,"ariaHidden":603},[602],[572,3087,3089,3093],{"className":3088},[607],[572,3090],{"className":3091,"style":3092},[611],"height:1.04em;vertical-align:-0.1328em;",[572,3094,3096],{"className":3095},[765,839],[572,3097,3099,3138],{"className":3098},[736,737],[572,3100,3102,3135],{"className":3101},[741],[572,3103,3105,3123],{"className":3104,"style":849},[745],[572,3106,3108,3111],{"className":3107,"style":778},[853],[572,3109],{"className":3110,"style":754},[753],[572,3112,3114,3117,3120],{"className":3113,"style":860},[765],[572,3115,680],{"className":3116},[765],[572,3118,683],{"className":3119,"style":867},[765,769],[572,3121,651],{"className":3122},[765,769],[572,3124,3125,3128],{"style":873},[572,3126],{"className":3127,"style":754},[753],[572,3129,3131],{"className":3130,"style":881},[880],[883,3132,3133],{"xmlns":885,"width":886,"height":887,"viewBox":888,"preserveAspectRatio":889},[891,3134],{"d":893},[572,3136,791],{"className":3137},[790],[572,3139,3141],{"className":3140},[741],[572,3142,3144],{"className":3143,"style":903},[745],[572,3145],{}," weglassen. Dann ist schon der Quotient falsch: ",[572,3148,3150,3176],{"className":3149},[575],[572,3151,3153],{"className":3152},[579],[581,3154,3155],{"xmlns":583},[585,3156,3157,3173],{},[588,3158,3159,3161,3163,3165,3167],{},[591,3160,692],{"stretchy":668},[641,3162,651],{},[641,3164,697],{"mathvariant":657},[641,3166,700],{},[702,3168,3169,3171],{},[591,3170,706],{"stretchy":668},[641,3172,651],{},[595,3174,3175],{"encoding":597},"(n\u002Fe)^n",[572,3177,3179],{"className":3178,"ariaHidden":603},[602],[572,3180,3182,3186,3189,3192,3195,3198],{"className":3181},[607],[572,3183],{"className":3184,"style":3185},[611],"height:1em;vertical-align:-0.25em;",[572,3187,692],{"className":3188},[812],[572,3190,651],{"className":3191},[765,769],[572,3193,697],{"className":3194},[765],[572,3196,700],{"className":3197},[765,769],[572,3199,3201,3204],{"className":3200},[924],[572,3202,706],{"className":3203},[924],[572,3205,3207],{"className":3206},[931],[572,3208,3210],{"className":3209},[736],[572,3211,3213],{"className":3212},[741],[572,3214,3217],{"className":3215,"style":3216},[745],"height:0.6644em;",[572,3218,3219,3222],{"style":3042},[572,3220],{"className":3221,"style":948},[753],[572,3223,3225],{"className":3224},[758,759,760,761],[572,3226,651],{"className":3227},[765,769,761]," allein ist um den Faktor ",[572,3230,3232,3253],{"className":3231},[575],[572,3233,3235],{"className":3234},[579],[581,3236,3237],{"xmlns":583},[585,3238,3239,3251],{},[588,3240,3241],{},[673,3242,3243],{},[588,3244,3245,3247,3249],{},[678,3246,680],{},[641,3248,683],{},[641,3250,651],{},[595,3252,3082],{"encoding":597},[572,3254,3256],{"className":3255,"ariaHidden":603},[602],[572,3257,3259,3262],{"className":3258},[607],[572,3260],{"className":3261,"style":3092},[611],[572,3263,3265],{"className":3264},[765,839],[572,3266,3268,3307],{"className":3267},[736,737],[572,3269,3271,3304],{"className":3270},[741],[572,3272,3274,3292],{"className":3273,"style":849},[745],[572,3275,3277,3280],{"className":3276,"style":778},[853],[572,3278],{"className":3279,"style":754},[753],[572,3281,3283,3286,3289],{"className":3282,"style":860},[765],[572,3284,680],{"className":3285},[765],[572,3287,683],{"className":3288,"style":867},[765,769],[572,3290,651],{"className":3291},[765,769],[572,3293,3294,3297],{"style":873},[572,3295],{"className":3296,"style":754},[753],[572,3298,3300],{"className":3299,"style":881},[880],[883,3301,3302],{"xmlns":885,"width":886,"height":887,"viewBox":888,"preserveAspectRatio":889},[891,3303],{"d":893},[572,3305,791],{"className":3306},[790],[572,3308,3310],{"className":3309},[741],[572,3311,3313],{"className":3312,"style":903},[745],[572,3314],{}," zu klein.",[2903,3317,3318,3319,3425,3426,3477,3478,3519,3520,3598],{},"Die grobe Form ",[572,3320,3322,3356],{"className":3321},[575],[572,3323,3325],{"className":3324},[579],[581,3326,3327],{"xmlns":583},[585,3328,3329,3353],{},[588,3330,3331,3333,3335,3337,3339,3341,3343,3345,3347,3349,3351],{},[641,3332,1314],{},[591,3334,646],{},[641,3336,651],{},[591,3338,669],{"stretchy":668},[591,3340,1323],{},[641,3342,651],{},[641,3344,1314],{},[591,3346,646],{},[641,3348,651],{},[591,3350,1334],{},[641,3352,651],{},[595,3354,3355],{"encoding":597},"\\ln n! \\approx n\\ln n - n",[572,3357,3359,3386,3416],{"className":3358,"ariaHidden":603},[602],[572,3360,3362,3365,3368,3371,3374,3377,3380,3383],{"className":3361},[607],[572,3363],{"className":3364,"style":746},[611],[572,3366,1314],{"className":3367},[731],[572,3369],{"className":3370,"style":805},[804],[572,3372,651],{"className":3373},[765,769],[572,3375,669],{"className":3376},[924],[572,3378],{"className":3379,"style":999},[804],[572,3381,1323],{"className":3382},[616],[572,3384],{"className":3385,"style":999},[804],[572,3387,3389,3392,3395,3398,3401,3404,3407,3410,3413],{"className":3388},[607],[572,3390],{"className":3391,"style":1398},[611],[572,3393,651],{"className":3394},[765,769],[572,3396],{"className":3397,"style":805},[804],[572,3399,1314],{"className":3400},[731],[572,3402],{"className":3403,"style":805},[804],[572,3405,651],{"className":3406},[765,769],[572,3408],{"className":3409,"style":1211},[804],[572,3411,1334],{"className":3412},[1215],[572,3414],{"className":3415,"style":1211},[804],[572,3417,3419,3422],{"className":3418},[607],[572,3420],{"className":3421,"style":1641},[611],[572,3423,651],{"className":3424},[765,769]," für genaue Werte nutzen. Bei ",[572,3427,3429,3447],{"className":3428},[575],[572,3430,3432],{"className":3431},[579],[581,3433,3434],{"xmlns":583},[585,3435,3436,3444],{},[588,3437,3438,3440,3442],{},[641,3439,651],{},[591,3441,711],{},[678,3443,2479],{},[595,3445,3446],{"encoding":597},"n = 100",[572,3448,3450,3468],{"className":3449,"ariaHidden":603},[602],[572,3451,3453,3456,3459,3462,3465],{"className":3452},[607],[572,3454],{"className":3455,"style":1641},[611],[572,3457,651],{"className":3458},[765,769],[572,3460],{"className":3461,"style":999},[804],[572,3463,711],{"className":3464},[616],[572,3466],{"className":3467,"style":999},[804],[572,3469,3471,3474],{"className":3470},[607],[572,3472],{"className":3473,"style":1012},[611],[572,3475,2479],{"className":3476},[765]," ergibt sie ",[572,3479,3481,3496],{"className":3480},[575],[572,3482,3484],{"className":3483},[579],[581,3485,3486],{"xmlns":583},[585,3487,3488,3493],{},[588,3489,3490],{},[678,3491,3492],{},"360,5",[595,3494,3495],{"encoding":597},"360{,}5",[572,3497,3499],{"className":3498,"ariaHidden":603},[602],[572,3500,3502,3505,3509,3515],{"className":3501},[607],[572,3503],{"className":3504,"style":2813},[611],[572,3506,3508],{"className":3507},[765],"360",[572,3510,3512],{"className":3511},[765],[572,3513,2148],{"className":3514},[2147],[572,3516,3518],{"className":3517},[765],"5"," statt ",[572,3521,3523,3548],{"className":3522},[575],[572,3524,3526],{"className":3525},[579],[581,3527,3528],{"xmlns":583},[585,3529,3530,3545],{},[588,3531,3532,3534,3536,3538,3540,3542],{},[641,3533,1314],{},[591,3535,646],{},[678,3537,2479],{},[591,3539,669],{"stretchy":668},[591,3541,1323],{},[678,3543,3544],{},"363,7",[595,3546,3547],{"encoding":597},"\\ln 100! \\approx 363{,}7",[572,3549,3551,3578],{"className":3550,"ariaHidden":603},[602],[572,3552,3554,3557,3560,3563,3566,3569,3572,3575],{"className":3553},[607],[572,3555],{"className":3556,"style":746},[611],[572,3558,1314],{"className":3559},[731],[572,3561],{"className":3562,"style":805},[804],[572,3564,2479],{"className":3565},[765],[572,3567,669],{"className":3568},[924],[572,3570],{"className":3571,"style":999},[804],[572,3573,1323],{"className":3574},[616],[572,3576],{"className":3577,"style":999},[804],[572,3579,3581,3584,3588,3594],{"className":3580},[607],[572,3582],{"className":3583,"style":2813},[611],[572,3585,3587],{"className":3586},[765],"363",[572,3589,3591],{"className":3590},[765],[572,3592,2148],{"className":3593},[2147],[572,3595,3597],{"className":3596},[765],"7",".",{"title":3600,"searchDepth":3601,"depth":3601,"links":3602},"",2,[3603,3604,3605],{"id":561,"depth":3601,"text":562},{"id":1680,"depth":3601,"text":1681},{"id":2897,"depth":3601,"text":2898},[3607,3610,3613,3616,3619,3622,3624,3627,3630],{"lhs":3608,"rhs":3609},"10!","3628800",{"lhs":3611,"rhs":3612},"round(sqrt(20*pi)*(10\u002Fexp(1))^10, 0)","3598696",{"lhs":3614,"rhs":3615},"round((10!\u002F(sqrt(20*pi)*(10\u002Fexp(1))^10) - 1)*100, 2)","0.84",{"lhs":3617,"rhs":3618},"round(sqrt(20*pi)*(10\u002Fexp(1))^10*(1 + 1\u002F120), 0)","3628685",{"lhs":3620,"rhs":3621},"round(log10(sqrt(200*pi)) + 100*log10(100\u002Fexp(1)), 2)","157.97",{"lhs":3623,"rhs":3621},"round(log10(100!), 2)",{"lhs":3625,"rhs":3626},"round(log(100!), 1)","363.7",{"lhs":3628,"rhs":3629},"round(100*log(100) - 100, 1)","360.5",{"lhs":3631,"rhs":714},"round((20! - sqrt(40*pi)*(20\u002Fexp(1))^20)\u002F1e16, 1)","n \\in \\mathbb{N},\\ n \\to \\infty","\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>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{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:0.5782em;vertical-align:-0.0391em;\">\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:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\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>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\to \\infty\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\">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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","stirling-formula","n! \\sim \\sqrt{2 \\pi n} \\left( \\frac{n}{e} \\right)^n","\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>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003Cmo>∼\u003C\u002Fmo>\u003Cmsqrt>\u003Cmrow>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsqrt>\u003Cmsup>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>e\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n! \\sim \\sqrt{2 \\pi n} \\left( \\frac{n}{e} \\right)^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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\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:1.8903em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9561em;\">\u003Cspan class=\"svg-align\" style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:0.833em;\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.9161em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\">\u003Cpath d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 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style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">e\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 mathnormal\">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:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose 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mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fstirling-formel",[],[3645,3646,3647],"factorial-permutations","euler-number-limit","binomial-coefficient",{"title":548,"description":3600},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fstirling-formel","Für große n ist n! ungefähr die Wurzel aus 2πn mal (n\u002Fe)ⁿ; der relative Fehler geht gegen 0.",[3652,3653,3654,3655],"stirling","fakultät","näherung","asymptotik",[3657,3661,3664,3667],{"symbol":3658,"meaning":3659,"symbolHtml":3660},"n!","Fakultät von n","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo 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class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":700,"meaning":3665,"symbolHtml":3666},"Eulersche Zahl, etwa 2,71828","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>e\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">e\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\">e\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":598,"meaning":3668,"symbolHtml":3669},"asymptotisch gleich, der Quotient beider Seiten geht gegen 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo>∼\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sim\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:0.3669em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∼\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","9aiU5RWcG8LAa193Ks27aGE0iU-nyCwKylo9kEfnMhs",[3672,3675,3678],{"stem":3673,"title":3674,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Feulersche-zahl-grenzwert","Eulersche Zahl als 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