Parameterized families of polylog integrals

Year 2021, Volume: 4 Issue: 4, 400 - 419, 13.12.2021

Anthony Sofo Necdet Batir

https://doi.org/10.33205/cma.1006384

Abstract

It is commonly known that integrals containing log-polylog integrands admit representations in terms
of special functions such as the Dirichlet eta and Dirichlet beta functions. We investigate two parameterized families
of such integrals and in a particular case demonstrate a connection with the Herglotz function. In the process of the
investigation we recover some known Euler sum equalities and discover some new identities.

Keywords

Harmonic number, gamma function, alternating harmonic number, Riemann zeta function, polylogarithm function, polygamma functions, linear Euler sums

Supporting Institution

none

Project Number

none

Thanks

Thank you

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