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.
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页数：12
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