The simplest proof of Jacobi's triple product identity originally due to Cauchy (1843) and Gauss (1866) is reviewed. In the same spirit, we prove by means of induction principle and finite difference method, a finite form of the quintuple product identity. Similarly, the induction principle will be used to give a new proof of another algebraic identity due to Guo and Zeng (2005), which can be considered as another finite form of the quintuple product identity.
La famosa identità di Jacobi riguardante il prodotto triplo viene esaminata grazie alle due dimostrazioni piu semplici dovute a Cauchy (1843) e Gauss (1866). Applicando il principio di induzione ed il metodo di differenze finite, lo stesso spirito ci conduce alla riconferma delle due forme finite dell'identità di prodotto quintuplo.
@article{BUMI_2007_8_10B_3_867_0,
author = {Wenchang Chu},
title = {Jacobi's Triple Product Identity and the Quintuple Product Identity},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {10-A},
year = {2007},
pages = {867-874},
zbl = {1183.33030},
mrnumber = {2507902},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_867_0}
}
Chu, Wenchang. Jacobi's Triple Product Identity and the Quintuple Product Identity. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 867-874. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_867_0/
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