کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4640226 1341267 2011 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions
چکیده انگلیسی

The main subject of this paper is the analysis of asymptotic expansions of Wallis quotient function Γ(x+t)Γ(x+s) and Wallis power function [Γ(x+t)Γ(x+s)]1/(t−s), when xx tends to infinity. Coefficients of these expansions are polynomials derived from Bernoulli polynomials. The key to our approach is the introduction of two intrinsic variables α=12(t+s−1) and β=14(1+t−s)(1−t+s) which are naturally connected with Bernoulli polynomials and Wallis functions. Asymptotic expansion of Wallis functions in terms of variables tt and ss and also αα and ββ is given. Application of the new method leads to the improvement of many known approximation formulas of the Stirling’s type.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 235, Issue 11, 1 April 2011, Pages 3315–3331
نویسندگان
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