Integral representations for the Gamma function, the Beta function, and the Double Gamma function
- 14 October 2009
- journal article
- research article
- Published by Informa UK Limited in Integral Transforms and Special Functions
- Vol. 20 (11), 859-869
- https://doi.org/10.1080/10652460902943519
Abstract
A variety of integral representations for some special functions have been developed. Here we aim at presenting certain (new or known) integral representations for , B(α, β), and by using some of the known integral representations of the Hurwitz (or generalized) Zeta function ζ(s, a). As a by-product of our main formulas, several integral representations for the Glaisher–Kinkelin constant A and the Psi (or Digamma) function ψ(a) are also given. Relevant connections of some of the results presented here with those obtained in earlier works are indicated. We also indicate the potential for the usefulness of these results.Keywords
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