Integral representations for the Gamma function, the Beta function, and the Double Gamma function

摘要

A variety of integral representations for some special functions have been developed. Here we aim at presenting certain (new or known) integral representations for log (a), B(α, β), and log 2(a) 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.