infinite series expansions
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1: 24.8 Series Expansions
2: 22.12 Expansions in Other Trigonometric Series and Doubly-Infinite Partial Fractions: Eisenstein Series
§22.12 Expansions in Other Trigonometric Series and Doubly-Infinite Partial Fractions: Eisenstein Series
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22.12.13
3: 25.2 Definition and Expansions
4: Bibliography S
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On integral representation of Weber’s parabolic cylinder function and its expansion into an infinite series.
J. Indian Math. Soc. (N. S.) 4, pp. 34–38.
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5: 31.11 Expansions in Series of Hypergeometric Functions
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§31.11(v) Doubly-Infinite Series
►Schmidt (1979) gives expansions of path-multiplicative solutions (§31.6) in terms of doubly-infinite series of hypergeometric functions. …6: 25.12 Polylogarithms
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►The cosine series in (25.12.7) has the elementary sum
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►For real or complex and the polylogarithm
is defined by
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►For each fixed complex the series defines an analytic function of for .
The series also converges when , provided that .
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►The notation was used for in Truesdell (1945) for a series treated in Jonquière (1889), hence the alternative name Jonquière’s function.
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7: 4.13 Lambert -Function
8: 16.11 Asymptotic Expansions
9: 2.1 Definitions and Elementary Properties
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►In those cases it is usually necessary to interpret each infinite series separately in the manner described above; that is, it is not always possible to reinterpret the asymptotic approximation as a single asymptotic expansion.
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10: 28.11 Expansions in Series of Mathieu Functions
§28.11 Expansions in Series of Mathieu Functions
►Let be a -periodic function that is analytic in an open doubly-infinite strip that contains the real axis, and be a normal value (§28.7). …The series (28.11.1) converges absolutely and uniformly on any compact subset of the strip . See Meixner and Schäfke (1954, §2.28), and for expansions in the case of the exceptional values of see Meixner et al. (1980, p. 33). … ►
28.11.7