Additional results on the series expansions of some trigonometric and hyperbolic functions (Q1373424)

The authors give a method for computing the coefficients of the series expansions of some trigonometric and hyperbolic functions. The method is based on interesting recurrence relations satisfied by the successive derivatives of these functions at \(x=0\) and on the construction of a triangular table, introduced by \textit{M. D. Atkinson} [Am. Math. Mon. 93, 387-389 (1986; Zbl 0603.65013)] for the Taylor expansion of \(\text{sec } x\) and \(\tan x\).