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28 March 2024
 
  » arxiv » 1606.8153

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Proof of a Conjecture of Z.-W. Sun on Trigonometric Series
Brian Y. Sun ; J.X. Meng ;
Date 27 Jun 2016
AbstractRecently, Z. W. Sun introduced a sequence $(S_n)_{ngeq 0}$, where $S_n=frac{inom{6n}{3n} inom{3n}{n}}{2(2n+1)inom{2n}{n}}$, and found one congruence and two convergent series on $S_n$ by { t{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 $sin(tarcsin(x))$ and $cos(tarcsin(x)).$
Source arXiv, 1606.8153
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