Gamma,Psi,Bernoulli Functions via Hurwitz Zeta Function
Number Theory
2010-01-19 v1
Abstract
Using three basic facts concerning Hurwitz zeta function,we give new natural proofs of the known results on Bernoulli polynomials,gamma function and also obtain Gauss' expression for Psi function at a rational point,all in a unified fashion.We also give a new proof of the relation between log gamma and derivative of the Hurwitz zeta function,including that of Stirling's expression for log gamma.
Cite
@article{arxiv.1001.2911,
title = {Gamma,Psi,Bernoulli Functions via Hurwitz Zeta Function},
author = {Vivek V. Rane},
journal= {arXiv preprint arXiv:1001.2911},
year = {2010}
}
Comments
14 pages