Generalized axisymmetric elliptic functions

Generalized Landen Transformation Formulas for Jacobi Elliptic Functions

Landen transformation formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by changing integration variables in elliptic integrals. We rediscover known results as well as obtain more generalized Landen formulas from a very different perspective, by making use of the recently obtained periodic solutions of physically ...

Trigonometric functions, elliptic functions, elliptic modular forms

Numerical approximation of axisymmetric positive solutions of semilinear elliptic equations in axisymmetric domains of R3

— We propose an algorithm which approaches positive solutions of elliptic semiliear equat boundary. n é ions with suhcritical nonlinearity in axisymmetric domains of M, with a degenerate

Discontinuities in an axisymmetric generalized thermoelastic problem

This paper deals with discontinuities analysis in the temperature, displacement, and stress fields of a thick plate whose lower and upper surfaces are traction-free and subjected to a given axisymmetric temperature distribution. The analysis is carried out under three thermoelastic theories. Potential functions together with Laplace and Hankel transform techniques are used to derive the solutio...

Heun functions versus elliptic functions

We present some recent progresses on Heun functions, gathering results from classical analysis up to elliptic functions. We describe Picard’s generalization of Floquet’s theory for differential equations with doubly periodic coefficients and give the detailed forms of the level one Heun functions in terms of Jacobi theta functions. The finite-gap solutions give an interesting alternative integr...