Summary: Symbolic and Numeric Computations of the
V. S. Adamchik
Department of Computer Science, Carnegie Mellon University, Pittsburgh, USA
This paper discusses some theoretical aspects and algorithms for high-precision
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.
In a sequence of papers published between 1899-1904, Barnes introduced and
studied (see ) a generalization of the classical Euler gamma function,
called the multiple gamma function n(z). The function n(z) satisfies the
following recurrence-functional equation [30,31]:
n+1(z + 1) =
, z C, n N
1(z) = (z)
n(1) = 1