A Generalization of Landen's Quadratic Transformation Formulas for Jacobi Elliptic Functions

Details A Generalization of Landen's Quadratic Transformation Formulas for Jacobi Elliptic Functions A Generalization of Landen's Quadratic Transformation Formulas for Jacobi Elliptic Functions

2002-04-30

arxiv.org/abs/math-ph/0204054v1

Physics

Mathematical Physics

11 pages

Scientific paper

Landen formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by making a suitable quadratic transformation of variables in elliptic integrals. We obtain and discuss significant generalizations of the celebrated Landen formulas. Our approach is based on some recently obtained periodic solutions of physically interesting nonlinear differential equations and numerous remarkable new cyclic identities involving Jacobi elliptic functions.

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