Displaying similar documents to “Zolotarev's proof of Gauss reciprocity and Jacobi symbols”

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.

Equiconvergence and equisummability of Jacobi series

Boychev, Georgi (2011)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 33C45, 40G05. In this paper we give some results concerning the equiconvergence and equisummability of series in Jacobi polynomials.

Concentration in the Nonlocal Fisher Equation: the Hamilton-Jacobi Limit

Benoît Perthame, Stephane Génieys (2010)

Mathematical Modelling of Natural Phenomena

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The nonlocal Fisher equation has been proposed as a simple model exhibiting Turing instability and the interpretation refers to adaptive evolution. By analogy with other formalisms used in adaptive dynamics, it is expected that concentration phenomena (like convergence to a sum of Dirac masses) will happen in the limit of small mutations. In the present work we study this asymptotics by using a change of variables that leads to a constrained Hamilton-Jacobi equation. We prove the convergence...