An asymptotic expansion of the double gamma function

Authors
Ferreira, C Lopez, JL
Citation
C. Ferreira et Jl. Lopez, An asymptotic expansion of the double gamma function, J APPROX TH, 111(2), 2001, pp. 298-314
Citations number
26
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF APPROXIMATION THEORY
ISSN journal
00219045 → ACNP
Volume
111
Issue
2
Year of publication
2001
Pages
298 - 314
Database
ISI
SICI code
0021-9045(200108)111:2<298:AAEOTD>2.0.ZU;2-1
Abstract
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 expans ion in decreasing powers of : and uniformly valid for \ Arg z \ < pi is der ived 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.