An Asymptotic Expansion of the Double Gamma Function

نویسندگان

  • Chelo Ferreira
  • José L. López
چکیده

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 z and uniformly valid for |Arg z|<? 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. 2001

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عنوان ژورنال:
  • Journal of Approximation Theory

دوره 128  شماره 

صفحات  -

تاریخ انتشار 2001