Multiple-angle formulas of generalized trigonometric functions with two parameters

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.

19 pages

References in corpus (2)

• A new form of the generalized complete elliptic integrals
• The basis property of generalized Jacobian elliptic functions

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• Applications of generalized trigonometric functions with two parameters II
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• Remarkable properties of the ${\text{sinc}}_{p,q}$ functions and related integrals
• Redheffer-type inequalities for generalized trigonometric functions