A Determinant of the Chudnovskys Generalizing the Elliptic Frobenius-Stickelberger-Cauchy Determinantal Identity

Abstract

D.V. Chudnovsky and G.V. Chudnovsky [CH] introduced a generalization of the Frobenius-Stickelberger determinantal identity involving elliptic functions that generalize the Cauchy determinant. The purpose of this note is to provide a simple essentially non-analytic proof of this evaluation. This method of proof is inspired by D. Zeilberger's creative application in [Z1].