Kórus, Péter Some applications of Retkes’ identity. (English) Zbl 1360.11148 Arch. Math. 104, No. 3, 217-222 (2015). Summary: We present some formulas for certain numeric sums related to the Riemann zeta function. The main tool used in our investigation is Retkes’ identity [Z. Retkes, Acta Sci. Math. 74, No. 1–2, 95–106 (2008; Zbl 1174.26008)]. We get a formula for \(\zeta(3)\) with the Euler beta function in it. Cited in 1 Document MSC: 11Y60 Evaluation of number-theoretic constants 11M06 \(\zeta (s)\) and \(L(s, \chi)\) 33B15 Gamma, beta and polygamma functions Keywords:Retkes’ identity; \(\zeta(3)\); binomial coefficients; alternating sums Citations:Zbl 1174.26008 Software:Mathematica PDFBibTeX XMLCite \textit{P. Kórus}, Arch. Math. 104, No. 3, 217--222 (2015; Zbl 1360.11148) Full Text: DOI Link References: [1] Retkes Z.: An extension of the Hermite-Hadamard inequality Acta Sci. Math. (Szeged) 74, 95-106 (2008) · Zbl 1174.26008 [2] Z. Retkes, Applications of the extended Hermite-Hadamard inequality, Journal of Inequalitites in Pure and Applied Mathematics (JIPAM) 7 (2006), article 24. · Zbl 1182.26026 [3] A. Jeffrey and D. Zwillinger, Table of Integrals, Series, and Products, Seventh Edition, Academic Press, 2007. · Zbl 1174.26008 [4] Wolfram Research, Inc., Mathematica, Version 10.0, Champaign, IL, 2014. 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.