Geodesic
Jacobi's Triple Product Identity and the Quintuple Product Identity
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 867-874 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
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     author = {Chu, Wenchang},
     title = {Jacobi's {Triple} {Product} {Identity} and the {Quintuple} {Product} {Identity}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {867--874},
     year = {2007},
     volume = {Ser. 8, 10B},
     number = {3},
     zbl = {1183.33030},
     mrnumber = {2507902},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a28/}
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Chu, Wenchang. Jacobi's Triple Product Identity and the Quintuple Product Identity. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 867-874. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a28/