Multiple Gamma Function and Its Application to Computation of Series

The multiple gamma function n, defined by a recurrence-functional equation as a generalization of the Euler gamma function, was originally introduced by Kinkelin, Glaisher, and Barnes around 1900. Today, due to the pioneer work of Conrey, Katz and Sarnak, interest in the multiple gamma function has been revived. This paper discusses some theoretical aspects of the ¡n function and their applications to summation of series and infinite products.