Parameterized families of polylog integrals

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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