Pade approximant related to the Wallis formula

被引：2

作者：

Lin, Long ^{[1
]}

Ma, Wen-Cheng ^{[2
]}

Chen, Chao-Ping ^{[1
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454000, Henan Province, Peoples R China

[2] Henan Polytech Univ, Coll Chem & Chem Engn, Jiaozuo City 454000, Henan Province, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2017年

关键词：

gamma function; psi function; Wallis ratio; inequality; approximation; GURLANDS FORMULA; INEQUALITIES; REFINEMENTS;

D O I：

10.1186/s13660-017-1406-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on the Pade approximation method, in this paper we determine the coefficients a(j) and b(j) such that pi = ((2n)!!/(2n - 1)!!)(2) {n(k) + a(1)n(k-1) + ... + a(k)/n(k+1) + b(1)n(k) + ... + b(k+1) + O(1/n(2k+3))}, n -> infinity, where k >= 0 is any given integer. Based on the obtained result, we establish a more accurate formula for approximating pi, which refines some known results.

引用

页数：12