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

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

2003-05-09

arxiv.org/abs/math/0305131v1

Integral Transforms and Special Functions, 14 (2003) 187-203

Mathematics

Classical Analysis and ODEs

15 pages

Scientific paper

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 $(e^{2\pi q
t}-1)^{-1}$, $(e^{2\pi q t}+1)^{-1}$, and $(\sinh(2\pi q t)^{-1}$.

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