Remarkable identities
Journal Title: Journal of Mathematics and Applications - Year 2014, Vol 37, Issue
Abstract
In the paper a number of identities involving even powers of the values of functions tangent, cotangent, secans and cosecans are proved. Namely, the following relations are shown: [formula], [formula], [formula], where m, n are positive integers, f is one of the functions: tangent, cotangent, secans or cosecans and w_f (x), v_f (x), [formula] are some polynomials from Q[x]. One of the remarkable identities is the following: [formula], provided m ≥ 1. Some of these identities are used to find, by elementary means, the sums of the series of the form [formula], where n is a fixed positive integer. One can also notice that Bernoulli numbers appear in the leading coefficients of the polynomials w_f (x), v_f (x) and [formula].
Authors and Affiliations
Jan Górowski, Jerzy Żabowski
Keywords
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