A Finite Form of Jacobi's Cubic Identity

William Y. C. Chen and Kathy Q. Ji
Center for Combinatorics, LPMC, Nankai University,
Tianjin 300071, P.R. China

Abstract

This paper is concerned with Jacobi's cubic identity which has many applications in number theory:

We obtain the following finite of form:

     (*)

We present a proof by using MacMahon's finite form of Jacobi's triple product identity. We also give an involution for the above finite form (*) in the framework of generalized Frobenius partition. Our involution is in the same spirit of the Jochi-Stanton involution..