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

2009/12/21 by Sekatskii, Sergey K.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0912.4116

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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