Multiple-angle formulas of generalized trigonometric functions with two parameters
Classical Analysis and ODEs
2019-03-12 v1 Analysis of PDEs
Abstract
Generalized trigonometric functions with two parameters were introduced by Dr\'{a}bek and Man\'{a}sevich to study an inhomogeneous eigenvalue problem of the -Laplacian. Concerning these functions, no multiple-angle formula has been known except for the classical cases and a special case discovered by Edmunds, Gurka and Lang, not to mention addition theorems. In this paper, we will present new multiple-angle formulas which are established between two kinds of the generalized trigonometric functions, and apply the formulas to generalize classical topics related to the trigonometric functions and the lemniscate function.
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Cite
@article{arxiv.1603.06709,
title = {Multiple-angle formulas of generalized trigonometric functions with two parameters},
author = {Shingo Takeuchi},
journal= {arXiv preprint arXiv:1603.06709},
year = {2019}
}
Comments
19 pages