Abstract
We establish some recurrence relations for the successive derivates atx=0 of some trigonometric and hyperbolic functions. We also construct an arithmetical triangle which gives immediately, by recurrence, the derivatives of the desidered order, of the functions sec, tan, cosec, cot, sech and tanh.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Bibliography
Atkinson M. D.,How to compute the series expansions of sec x and tan x, Amer. Math.,5 (1986), 387–389.
Gardiner A.,Infinite processes, Springer Verlag, pag. 284.
Donald E. Knuth., Thomas J. Buckholtz.,Computation of Tangent, Euler, and Bernoulli Numbers, Math. of Comp.,21 (1967), 663–668.
Laforgia A.,Inequalities for the Bernoulli and Euler Numbers, Boll. U.M.I. (3),17A (1980), 98–101.
Robert A. Leslie.,How not to repeatedly differentiate a reciprocal, Amer. Math. Month., (1991), (733–735).
Li-Chien Shen.,On the Zeros of tan(k)z, Amer. Math. Month., (1991), 525–527.
Author information
Authors and Affiliations
Additional information
Work supported by M.U.R.S.T. and C.N.R.
Rights and permissions
About this article
Cite this article
Palmisani, C., Rizzi, B. Additional results on the series expansions of some trigonometric and hyperbolic functions. Rend. Circ. Mat. Palermo 45, 173–188 (1996). https://doi.org/10.1007/BF02844484
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02844484