On the use of the variable change w=exp(u) to establish novel integral representations of the Riemann zeta(s,a) -function, incomplete gamma- function, confluent hypergeometric Phi-function and beta function
Functional Analysis
2010-01-15 v2
Abstract
The variable change w=exp(u) is applied to establish novel integral representations of the incomplete gamma-function, hypergeometric F-function,confluent hypergeometric /Phi-function and beta-function, and to analyze these functionsas as well as the Riemann /zeta(s,a)-function. In particular, using these representations we give a pedagogically instructive proof of the well known approximate functional relation for the Riemann /zeta-function and derive Hurwitz representation of the /zeta(s,a)-function.
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Cite
@article{arxiv.0912.4116,
title = {On the use of the variable change w=exp(u) to establish novel integral representations of the Riemann zeta(s,a) -function, incomplete gamma- function, confluent hypergeometric Phi-function and beta function},
author = {Sergey K. Sekatskii},
journal= {arXiv preprint arXiv:0912.4116},
year = {2010}
}