summation formulas
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21—27 of 27 matching pages
21: 18.20 Hahn Class: Explicit Representations
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§18.20(i) Rodrigues Formulas
… ► … ►Here we use as convention for (16.2.1) with , , and that the summation on the right-hand side ends at . …22: Bibliography K
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Connection formulae for the first Painlevé transcendent in the complex domain.
Lett. Math. Phys. 27 (4), pp. 243–252.
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The Hahn polynomials, formulas and an application.
Scripta Math. 26, pp. 33–46.
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On formulas involving both the Bernoulli and Fibonacci numbers.
Scripta Math. 23, pp. 27–35.
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An extension of Saalschütz’s summation theorem for the series
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Integral Transforms Spec. Funct. 24 (11), pp. 916–921.
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The addition formula for Laguerre polynomials.
SIAM J. Math. Anal. 8 (3), pp. 535–540.
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23: Bibliography
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Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.
National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
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Summations and transformations for basic Appell series.
J. London Math. Soc. (2) 4, pp. 618–622.
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Special value of the hypergeometric function and connection formulae among asymptotic expansions.
J. Indian Math. Soc. (N.S.) 51, pp. 161–221.
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Formulas for higher derivatives of the Riemann zeta function.
Math. Comp. 44 (169), pp. 223–232.
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Bernoulli’s power-sum formulas revisited.
Math. Gaz. 90 (518), pp. 276–279.
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24: 17.6 Function
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►This reverses the order of summation in (17.6.2):
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►Related formulas are (17.7.3), (17.8.8) and
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►For similar formulas see Verma and Jain (1983).
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25: Bibliography R
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Fourier analysis and signal processing by use of the Möbius inversion formula.
IEEE Trans. Acoustics, Speech, Signal Processing 38, pp. 458–470.
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Research Institute for Symbolic Computation, Hagenberg im Mühlkreis, Austria.
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Another proof of the triple sum formula for Wigner -symbols.
J. Math. Phys. 40 (12), pp. 6689–6691.
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26: 25.11 Hurwitz Zeta Function
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§25.11(iii) Representations by the Euler–Maclaurin Formula
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25.11.5
, , , .
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25.11.10
, .
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25.11.28
, , .
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25.11.43
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