Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions

• Published in: Journal of computational and applied mathematics Vol. 235; no. 11; pp. 3315 - 3331
• Main Authors: BURIC, Tomislav, ELEZOVIC, Neven
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.04.2011; Elsevier
• Subjects: Algebra; Approximation; Asymptotic expansion; Asymptotic expansions; Bernoulli polynomials; Computation; Exact sciences and technology; Gamma function; Infinity; Mathematical analysis; Mathematical models; Mathematics; Number theory; Numerical analysis; Numerical analysis. Scientific computation; Quotients; Sciences and techniques of general use; Special functions; Stirling formula; Wallis power function; Wallis quotient; secondary; Wallis quotient; Asymptotic expansion; Stirling formula; Bernoulli polynomials; Gamma function; Wallis power function; primary; Polynomial; primary 33B15; Approximation; 41A60; 57Q55; 11B68; 33F05; Polynomial function; secondary 40A25; Numerical analysis; Applied mathematics

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 x tends to infinity. Coefficients of these expansions are polynomials derived from Bernoulli polynomi...