Journal
JOURNAL OF APPROXIMATION THEORY
Volume 111, Issue 2, Pages 298-314Publisher
ACADEMIC PRESS INC
DOI: 10.1006/jath.2001.3578
Keywords
Barnes double gamma function; asymptotic expansions
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The Barnes double gamma function G(z) is considered for large argument z. A new integral representation is obtained for log G(z). An asymptotic expansion in decreasing powers of : and uniformly valid for \ Arg z \ < pi is derived from this integral. The expansion is accompanied by an error bound at any order of the approximation. Numerical experiments show that this bound is very accurate for real z. The accuracy of the error bound decreases for increasing Arg z. (C) 2001 Academic Press.
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