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CONTRIBUTIONS TO THE THEORY OF THE BARNES FUNCTION
 

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 high-precision computation of the Barnes
gamma function and Glaisher's constant are also discussed
1. Introduction
In a sequence of papers published between 1899-1904, 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 recurrence-functional 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