On some families of integrals solvable in terms of polygamma and negapolygamma functions

Boros, George; Espinosa, Olivier; Moll, Victor H.

On some families of integrals solvable in terms of polygamma and negapolygamma functions

Authors

Boros, George

Espinosa, Olivier

Moll, Victor H.

Description

Beginning with Hermite's integral representation of the Hurwitz zeta function, we derive explicit expressions in terms of elementary, polygamma, and negapolygamma functions for several families of integrals of the type $\int_0^\infty f(t)K(q,t)dt$ with kernels $K(q,t)$ equal to $(e^{2πq t}-1)^{-1}$, $(e^{2πq t}+1)^{-1}$, and $(\sinh(2πq t)^{-1}$.
15 pages