The Multiple Gamma-Functions and the Log-Gamma Integrals

الملخص EN

In this paper, which is a companion paper to [W], starting from the Euler integral which appears in a generalization of Jensen’s formula, we shall give a closed form for the integral of log Γ(1±t).

This enables us to locate the genesis of two new functions A1/a and C1/a considered by Srivastava and Choi.

We consider the closely related function A(a) and the Hurwitz zeta function, which render the task easier than working with the A1/a functions themselves.

We shall also give a direct proof of Theorem 4.1, which is a consequence of [CKK, Corollary 1.1], though.