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Transformation on infinite double series and applications to harmonic number identities. (English) Zbl 1062.33022

Summary: A general transformation formula between an infinite double series and an infinite single sum is established, which specializes to several infinite double series identities, including a recent one due to R. Lyons, P. Paule and A. Riese [Commun. Comput. 13, 327–333 (2002; Zbl 1011.33003).

MSC:

33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
11B68 Bernoulli and Euler numbers and polynomials
05A19 Combinatorial identities, bijective combinatorics

Citations:

Zbl 1011.33003

Software:

MultiSum
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Full Text: DOI

References:

[1] Bailey, W.N.: Generalized Hypergeometric Series. Cambridge University Press, Cambridge, 1935 · Zbl 0011.02303
[2] Krattenthaler, C.: Hypergeometric proof of a curious identity of Lyons, Paule and Riese. Preprint, http://www.mat.univie.ac.at/ · Zbl 1063.33006
[3] Lyons, R., Paule, P., Riese, A.: A computer proof of a series evaluation in terms of harmonic number. Appl. Algebra Engrg. Commun. Comput. 13(4), 327-333 (2002) · Zbl 1011.33003 · doi:10.1007/s00200-002-0107-z
[4] Lyons, R., Steif, J.: Stationary determinantal process: Phase multiplicity, Bernoullicity, entropy and domination. Duke Math. J. 120(3), 515-575 (2003) · Zbl 1068.82010
[5] Slater, I.J.: Generalized Hypergeometric Functions. Cambridge University Press, Cambridge, 1966 · Zbl 0135.28101
[6] Stromberg, K.R.: An Introduction to Classical Real Analysis. Wadsworth, INC. Belmont, California, 1981 · Zbl 0454.26001
[7] Weisstein, E.W.: Dirichlet Beta Function. From MathWorld [A Wolfram Web Resource]: http://mathworld.wolfram.com/DirichletBetaFunction.html
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