2023/02/20 by Alexander Dyachenko, Dyachenko, Alexander, Dmitrii Karp +1
Computer Science · Mathematics · #33B10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2302.10333
openalex publication_date 2023/02/20 · openalex created_date 2023/02/24 · openalex updated_date 2026/07/28
Known already to the ancient Greeks, today trigonometric identities come in a large variety of tastes and flavours. In this large family there is a subfamily of interpolation-like identities discovered by Hermite and revived rather recently in two independent papers, one by Wenchang Chu and the other by Warren Johnson exploring various forms and generalizations of Hermite's results. The goal of this work inspired by these two articles is twofold. The first goal is to fill a gap in the references from the above papers and exhibit various trigonometric identities discovered by Meijer, Nørlund and Braaksma between 1940 and 1962 in the context of analytic continuation of Mellin-Barnes integrals and relations between different solutions of the generalized hypergeometric differential equation. Our second goal is to present some extensions of Chu's and Johnson's results by combining them with the ideas of Meijer and Braaksma adding certain sum manipulations and facts from the complex analysis. We unify and systematize various known and new identities and illustrate our results with numerous explicit examples.