Mathematics – Functional Analysis
Scientific paper
2009-12-21
Mathematics
Functional Analysis
Scientific paper
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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