Jacobi's Triple Product Identity and the Quintuple Product Identity

Wenchang Chu

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 867-874
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Chu, Wenchang. "Jacobi's Triple Product Identity and the Quintuple Product Identity." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 867-874. <http://eudml.org/doc/290428>.

@article{Chu2007,
abstract = {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.},
author = {Chu, Wenchang},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {867-874},
publisher = {Unione Matematica Italiana},
title = {Jacobi's Triple Product Identity and the Quintuple Product Identity},
url = {http://eudml.org/doc/290428},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Chu, Wenchang
TI - Jacobi's Triple Product Identity and the Quintuple Product Identity
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 867
EP - 874
AB - 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 - eng
UR - http://eudml.org/doc/290428
ER -

References

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