Chu, Wenchang; De Donno, Livia Transformation on infinite double series and applications to harmonic number identities. (English) Zbl 1062.33022 Appl. Algebra Eng. Commun. Comput. 15, No. 5, 339-348 (2005). 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 Keywords:Harmonic Number; Bernoulli Number; Euler Number; Catalan Constant; Binomial Coefficient Identity; Double Series Transformation Citations:Zbl 1011.33003 Software:MultiSum PDFBibTeX XMLCite \textit{W. Chu} and \textit{L. De Donno}, Appl. Algebra Eng. Commun. Comput. 15, No. 5, 339--348 (2005; Zbl 1062.33022) 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.