Unification of the quintuple and septuple product identities.
Chu, Wenchang, Yan, Qinglun (2007)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “Polynomial identities which imply identities of Euler and Jacobi”
Unification of the quintuple and septuple product identities.
The generating function for the Jacobi polynomial
L. Carlitz (1967)
Rendiconti del Seminario Matematico della Università di Padova
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Jacobi's Triple Product Identity and the Quintuple Product Identity
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.
Construction of the lowest-order recurrence relation for the Jacobi coefficients
S. Lewanowicz (1983)
Applicationes Mathematicae
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Consequences of a sextuple-product identity.
Ewell, John A. (1987)
International Journal of Mathematics and Mathematical Sciences
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GO++: A modular Lagrangian/Eulerian software for Hamilton Jacobi equations of geometric optics type
Jean-David Benamou, Philippe Hoch (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.