Parameterized families of polylog integrals
Authors : Anthony Sofo, Necdet Batir
Pages : 400-419
Doi:10.33205/cma.1006384
View : 9 | Download : 6
Publication Date : 2021-12-13
Article Type : Research
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