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arXiv · 1603.06709

Multiple-angle formulas of generalized trigonometric functions with two parameters

Shingo Takeuchi
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Abstract

Generalized trigonometric functions with two parameters were introduced by Drábek and Manásevich to study an inhomogeneous eigenvalue problem of the $p$-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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Shingo Takeuchi. 2016-03-22. Multiple-angle formulas of generalized trigonometric functions with two parameters. https://doi.org/10.1016/j.jmaa.2016.06.074

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