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Article overview
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A new trigonometric identity with applications | | Zhi-Wei Sun
; Hao Pan
; | | Date: |
18 Jul 2019 | | Abstract: | In this paper we obtain a new curious identity involving trigonometric
functions. Namely, for any positive odd integer $n$ we show that
$$sum_{k=1}^n(-1)^k(cot kx)sin k(n-k)x=frac{1-n}2.$$ Consequently, for any
positive odd integer $n$ and positive integer $m$ we have
$$sum_{k=1}^n(-1)^kk^{2m}B_{2m+1}left(frac{n-k}2
ight)=0,$$ where $B_j(x)$
denotes the Bernoulli polynomial of degree $j$. | | Source: | arXiv, 1907.8118 | | Services: | Forum | Review | PDF | Favorites | |
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