Parameterized families of polylog integrals

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Constructive Mathematical Analysis
Volume:4 Issue:4
Parameterized families of polylog integrals

Parameterized families of polylog integrals

Authors : Anthony SOFO, Necdet BATİR

Pages : 400-419

Doi:10.33205/cma.1006384

View : 36 | Download : 11

Publication Date : 2021-12-13

Article Type : Research Paper

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

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