On some families of integrals solvable in terms of polygamma and negapolygamma functions
Abstract
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 $(\sinh(2\pi q t)^{-1}$.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- May 2003
- DOI:
- 10.48550/arXiv.math/0305131
- arXiv:
- arXiv:math/0305131
- Bibcode:
- 2003math......5131B
- Keywords:
-
- Mathematics - Classical Analysis and ODEs;
- 33B99;
- 11M35
- E-Print:
- 15 pages