کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607861 1337887 2009 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A simplification of Laplace’s method: Applications to the Gamma function and Gauss hypergeometric function
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
A simplification of Laplace’s method: Applications to the Gamma function and Gauss hypergeometric function
چکیده انگلیسی

The main difficulties in the Laplace’s method of asymptotic expansions of integrals are originated by a change of variables. We propose a variant of the method which avoids that change of variables and simplifies the computations. On the one hand, the calculation of the coefficients of the asymptotic expansion is remarkably simpler. On the other hand, the asymptotic sequence is as simple as in the standard Laplace’s method: inverse powers of the asymptotic variable. New asymptotic expansions of the Gamma function Γ(z)Γ(z) for large zz and the Gauss hypergeometric function 2F1(a,b,c;z)2F1(a,b,c;z) for large bb and cc are given as illustrations. An explicit formula for the coefficients of the classical Stirling expansion of Γ(z)Γ(z) is also given.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 161, Issue 1, November 2009, Pages 280–291
نویسندگان
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