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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 | Abstract: | Recently, 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 | Services: | Forum | Review | PDF | Favorites |
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