Some properties of the generalized Jacobian elliptic functions

Abstract

This paper deals with some aspects of the differential and integral calculus for the generalized Jacobian elliptic functions. They play an important role in some bifurcation problems involving the p-Laplacian. Differentiation formulas for a dozen members of the family of functions under discussion are obtained. Several formulas for the indefinite integrals of the generalized Jacobian elliptic functions are also derived.

Keywords:

• generalized Jacobian elliptic functions
• generalized trigonometric and generalizedhyperbolic functions
• R-hypergeometric functions

AMS Subject Classification:

• 33E05
• 26A06

Disclosure statement

No potential conflict of interest was reported by the author.