infinite series
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31—40 of 68 matching pages
31: 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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32: 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
33: 9.7 Asymptotic Expansions
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►In (9.7.9)–(9.7.12) the th error term in each infinite series is bounded in magnitude by the first neglected term and has the same sign, provided that the following term in the series is of opposite sign.
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34: Bibliography K
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Theorie und Anwendung der unendlichen Reihen.
4th edition, Die Grundlehren der mathematischen Wissenschaften, Band 2, Springer-Verlag, Berlin-Heidelberg (German).
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35: Errata
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Subsection 25.2(ii) Other Infinite Series
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36: 2.11 Remainder Terms; Stokes Phenomenon
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►Secondly, the asymptotic series represents an infinite class of functions, and the remainder depends on which member we have in mind.
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37: 27.14 Unrestricted Partitions
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►The 24th power of in (27.14.12) with is an infinite product that generates a power series in with integer coefficients called Ramanujan’s tau function
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38: 27.4 Euler Products and Dirichlet Series
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►In this case the infinite product on the right (extended over all primes ) is also absolutely convergent and is called the Euler product of the series.
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39: 18.38 Mathematical Applications
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►In consequence, expansions of functions that are infinitely differentiable on in series of Chebyshev polynomials usually converge extremely rapidly.
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40: 1.3 Determinants, Linear Operators, and Spectral Expansions
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►These have the property that the double series
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