Elliptic Polynomials

Abstract

This talk is about sequences of polynomials $\{P_n(x)\}$, some of which are orthogonal, that come from generating functions $\exp(xf(t))$, where f is either an odd Jacobi elliptic function or an odd elliptic integral of the first kind. One of the results of the study is information about the coefficients of the Maclaurin expansion of an odd Jacobi elliptic function such as $\sn(x,k)$. This is part of joint work with John Lomont that will soon appear in a book titled "Elliptic Polynomials" to be published by Chapman & Hall/CRC Press.