Chu–Vandermonde sums (first and second)
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11—20 of 517 matching pages
11: 10.31 Power Series
12: 22.11 Fourier and Hyperbolic Series
13: 14.28 Sums
14: 14.7 Integer Degree and Order
15: Bibliography D
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Sums of products of Bernoulli numbers.
J. Number Theory 60 (1), pp. 23–41.
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A simple sum formula for Clebsch-Gordan coefficients.
Lett. Math. Phys. 5 (3), pp. 207–211.
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On Vandermonde’s theorem, and some more general expansions.
Proc. Edinburgh Math. Soc. 25, pp. 114–132.
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Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter.
SIAM J. Math. Anal. 21 (4), pp. 995–1018.
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16: 22.12 Expansions in Other Trigonometric Series and Doubly-Infinite Partial Fractions: Eisenstein Series
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22.12.2
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►The double sums in (22.12.2)–(22.12.4) are convergent but not absolutely convergent, hence the order of the summations is important.
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22.12.8
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22.12.11
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22.12.12
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17: 10.38 Derivatives with Respect to Order
18: 28.24 Expansions in Series of Cross-Products of Bessel Functions or Modified Bessel Functions
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►Also, with and denoting the modified Bessel functions (§10.25(ii)), and again with ,
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28.24.10
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28.24.11
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28.24.12
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28.24.13
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19: 19.5 Maclaurin and Related Expansions
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19.5.4_2
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►Coefficients of terms up to are given in Lee (1990), along with tables of fractional errors in and , , obtained by using 12 different truncations of (19.5.6) in (19.5.8) and (19.5.9).
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19.5.8
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19.5.9
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►Series expansions of and are surveyed and improved in Van de Vel (1969), and the case of is summarized in Gautschi (1975, §1.3.2).
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