Tangent power sums and their applications

Vladimir Shevelev; Peter J. C. Moses

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arXiv · 1207.0404

Tangent power sums and their applications

Vladimir Shevelev·Peter J. C. Moses

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Abstract

For integer $m, p,$ we study tangent power sum $\sum^m_{k=1}\tan^{2p}\frac{πk}{2m+1}.$ We prove that, for every $m, p,$ it is integer, and, for a fixed p, it is a polynomial in $m$ of degree $2p.$ We give recurrent, asymptotical and explicit formulas for these polynomials and indicate their connections with Newman's digit sums in base $2m.$

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Vladimir Shevelev, Peter J. C. Moses. 2014-07-31. Tangent power sums and their applications. https://arxiv.org/abs/1207.0404

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