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On the one hand the Fermi-Dirac and Bose-Einstein functions have beenextended in such a way that they are closely related to the Riemann and otherzeta functions. On the other hand the Fourier transform representation of thegamma and generalized gamma functions proved useful in deriving variousintegral formulae for these functions. In this paper we use the Fouriertransform representation of the extended functions to evaluate integrals ofproducts of these functions. In particular we evaluate some integralscontaining the Riemann and Hurwitz zeta functions, which had not been evaluatedbefore.

Fourier Transform Representation of the Extended Fermi-Dirac and  Bose-Einstein Functions with Applications to the Family of the Zeta and  Related Functions