关于雅克比等式证明一些恒等式的一个注释

摘要

在两个无穷乘积等式的证明中涉及到六重乘积恒等式和著名的雅克比三重乘积恒等式,这些恒等式最早出现在约翰·尤厄尔的文章中,它可以看做是雅克比θ函数定理的注释.本文利用不同与约翰·尤厄尔的方法,给出了另外两个恒等式的证明,其中一个等式暗含雅克比恒等式.在运用函数等式法和一些分析的技巧证明这两个恒等式的过程中,并给出了一个推论的证明.%Two infinite product identities involving sextuple product identity and celebrated Jacobi triple product identity,first derived by John A.Ewell in his thesis,is the Jacobian theory of θfunctions of this note.These two identities,including one that implies Jacobi's identity,are proved to be different from John A.Ewell's method.This article combines the functional equation means and some analytically technique to prove these equations.And a corollary is consequently derived.