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.

Authors: Sergey K. Sekatskii
Subjects: Functional Analysis

link: http://arxiv.org/abs/0912.4116
Abstract

The variable change w=exp(u) is applied to establish novel integral
representations of the Riemann zeta(s,a)-function, incomplete gamma- function,
confluent hypergeometric Phi-function and beta-function. 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.

Primary-links

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.

User login