Trigonometric identities: from Hermite via Meijer, Nørlund, and Braaksma to Chu and Johnson and beyond

Known already to the ancient Greeks, today trigonometric identities come in a large variety of tastes and flavours. In this family there is subfamily interpolation-like discovered by Hermite revived rather recently two independent papers, one Wenchang Chu other Warren Johnson exploring various forms generalizations Hermite’s results. The goal work inspired these articles twofold. first fill gap references from above papers exhibit Meijer, Nørlund Braaksma between 1940 1962 context analytic continuation Mellin-Barnes integrals relations different solutions generalized hypergeometric differential equation. Our second present some extensions Chu’s Johnson’s results combining them with ideas Meijer adding certain sum manipulations facts complex analysis. We unify systematize known new illustrate our numerous explicit examples.