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Some applications of Retkes’ identity. (English) Zbl 1360.11148

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.

MSC:

11Y60 Evaluation of number-theoretic constants
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
33B15 Gamma, beta and polygamma functions

Citations:

Zbl 1174.26008

Software:

Mathematica
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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.
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