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 FrobeniusStickelberger 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]. AMS Subject Classification: Primary 05A, 11A, 15A One of the most famous alternants is the Cauchy determinant which is only a special case of a determinant with symbolic entries: (1) det 1 xi - yj 1i,jn = (-1)n(n-1)/2 i<j(xi - xj)(yi - yj) n i=1 n j=1(xi - yj) . This expression lends itself to explicit formulas in Pad

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Tewodros Amdeberhan
• Keywords: Cauchy, COMBINATORICS 2000, Determinant, Elliptic Function