Proof of a Conjecture of Z.-W. Sun on Trigonometric Series

被引：0

作者：

Sun, Brian Y. ^{[1
]}

Meng, J. X. ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China

来源：

UTILITAS MATHEMATICA | 2017年 / 102卷

关键词：

Divisibility; Congruences; Trigonometric series; Convergent series;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently, Z. W. Sun introduced a sequence (S-n)n >= 0, where Sn=((6n)(3n))((3n)(n))/2(2n+1)((2n)(n)), and found one congruence and two convergent series on Sn by {\tt{Mathematica. Furthermore, he proposed some related conjectures. In this paper, we first give analytic proofs of his two convergent series and then confirm one of his conjectures by invoking series expansions of sin(t arcsin(x)) and cos(t arcsin(x)).

引用

页码：223 / 229

页数：7

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