Tangent power sums and their applications
Vladimir Shevelev, Peter J. C. Moses · arXiv (Cornell University) · 2012
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 $2m.$