Summary: CONTRIBUTIONS TO THE THEORY OF THE
BARNES FUNCTION
V. S. ADAMCHIK
Abstract. This paper presents a family of new integral represen­
tations and asymptotic series of the multiple gamma function. The
numerical schemes for high­precision computation of the Barnes
gamma function and Glaisher's constant are also discussed
1. Introduction
In a sequence of papers published between 1899­1904, Barnes intro­
duced and studied (see [9, 10, 11, 12]) a generalization of the classi­
cal Euler gamma function, called the multiple gamma function # n (z).
The function # n (z) satisfies the following recurrence­functional equa­
tion [31, 32]:
(1)
# n+1 (z + 1) =
# n+1 (z)
# n (z)
, z # C, n # N,
# 1 (z) = #(z),
# n (1) = 1,

Source: Adamchik, Victor - School of Computer Science, Carnegie Mellon University

Collections: Computer Technologies and Information Sciences