 
Summary: Symbolic and Numeric Computations of the
Barnes Function
V. S. Adamchik
Department of Computer Science, Carnegie Mellon University, Pittsburgh, USA
Abstract
This paper discusses some theoretical aspects and algorithms for highprecision
computation of the Barnes gamma function.
Key words: Barnes function; Gamma function; Riemann zeta function; Hurwitz
zeta function; Stirling numbers; harmonic numbers; Glaisher's constant.
1 Introduction
In a sequence of papers published between 18991904, Barnes introduced and
studied (see [811]) a generalization of the classical Euler gamma function,
called the multiple gamma function n(z). The function n(z) satisfies the
following recurrencefunctional equation [30,31]:
n+1(z + 1) =
n+1(z)
n(z)
, z C, n N
1(z) = (z)
n(1) = 1
