Tangent power sums and their applications

Abstract

For integer $m,p,$ we study tangent power sum ${\sum }_{k=1}^m{\tan }^{2p}\frac{\pi k}{2m+1}.$ 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 $2m.$

14 pages. Addition of reference: A.M. and I.M. Yaglom (1953)

References in corpus (1)

• Two algorithms for evaluation of the Newman digit sum, and a new proof of Coquet's theorem

Cited by in corpus (1)

• An integral approach to the Gardner-Fisher and untwisted Dowker sums