### Unification of the quintuple and septuple product identities.

Chu, Wenchang, Yan, Qinglun (2007)

The Electronic Journal of Combinatorics [electronic only]

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Chu, Wenchang, Yan, Qinglun (2007)

The Electronic Journal of Combinatorics [electronic only]

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Chan, Hei-Chi (2005)

International Journal of Mathematics and Mathematical Sciences

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Patkowski, Alexander E. (2010)

Integers

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Melham, Ray S. (2010)

Integers

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Michael Hirschhorn (1977)

Acta Arithmetica

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Bruce C. Berndt, Hamza Yesilyurt (2005)

Acta Arithmetica

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Ewell, John A. (1991)

International Journal of Mathematics and Mathematical Sciences

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Wenchang Chu (2007)

Bollettino dell'Unione Matematica Italiana

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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.

Prodinger, Helmut (2008)

Integers

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Paule, Peter (1994)

The Electronic Journal of Combinatorics [electronic only]

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Robert Bartoszyński (1974)

Colloquium Mathematicae

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Liu, Zhi-Guo (2001)

Integers

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Grossman, George, Tefera, Akalu, Zeleke, Aklilu (2006)

International Journal of Mathematics and Mathematical Sciences

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