Abstract
We give a simple proof of the well-known quintuple product identity. The strategy of our proof is similar to a proof of Jacobi (ascribed to him by Enneper) for the triple product identity.
Highlights
The well-known quintuple product identity can be stated as follows
We give a simple proof of the well-known quintuple product identity
The strategy of our proof is similar to a proof of Jacobi for the triple product identity
Summary
The well-known quintuple product identity can be stated as follows. For z = 0 and |q| < 1, ∞f (z, q) : = 1 − q2n+2 1 − zq2n+1 n=0 − 1 z q2n+1 =q3n2+n z3nq−3n − z−3n−1q3n+1 . n=−∞ 1 − z2q4n 1 z2 q4n+4. We give a simple proof of the well-known quintuple product identity. The strategy of our proof is similar to a proof of Jacobi (ascribed to him by Enneper) for the triple product identity. 1. Introduction The well-known quintuple product identity can be stated as follows. The quintuple identity has a long history and, as Berndt [5] points out, it is difficult to assign priority to it.
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