Infinite series around multinomial coefficients and harmonic numbers. (English) Zbl 1527.11066

Chu, Wenchang

Kodai Math. J. 46, No. 2, 115-144 (2023).

The purpose of this paper is to find corollaries of the Gauss summation theorem for \(_2\)F\(_ 1\)-series involving harmonic numbers and multinomial coefficients. To this aim, a formula for the power series expansion of a certain Gamma function quotient is stated. The main theorem is an infinite series evaluation of a series of harmonic numbers with Pochhammer symbol coefficients.

Reviewer: Thomas Ernst (Uppsala)

MSC:

11M06	\(\zeta (s)\) and \(L(s, \chi)\)
11B65	Binomial coefficients; factorials; \(q\)-identities
33C20	Generalized hypergeometric series, \({}_pF_q\)
65B10	Numerical summation of series

Keywords:

hypergeometric series; Gauss summation theorem; \(\Gamma \)-function; harmonic numbers; multinomial coefficient

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