2022•Applicable Analysis and Discrete MathematicsOpen access

Euler sums of generalized harmonic numbers and connected extensions

Mümün Can, Levent Kargın, Ayhan Dil, Gültekin Soylu

Abstract

This paper presents the evaluation of the Euler sums of generalized hyper-harmonic numbers Hn(p,q) in terms of the famous Euler sums of generalized harmonic numbers. Moreover, several infinite series, whose terms consist of certain harmonic numbers and reciprocal binomial coefficients, are evaluated in terms of the Riemann zeta values.

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Key concepts: Harmonic number, Mathematics, Euler's formula, Proof of the Euler product formula for the Riemann zeta function, Binomial coefficient, Euler summation, Harmonic, Euler number (physics)