The Multiple Gamma-Functions and the Log-Gamma Integrals

Abstract

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 . This enables us to locate the genesis of two new functions and 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 functions themselves. We shall also give a direct proof of Theorem 4.1, which is a consequence of [CKK, Corollary 1.1], though.