Far Eastern Mathematical Journal

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On the connection between hyperelliptic systems of sequences and functions

Illarionov A.A., Romanov M.A.

2017, issue 2, P.

We study the connection between 1-periodic solutions of the functional equation $$ f(x+y)g(x-y)=\sum_{j=1}^N\varphi_j(x)\psi_j(y) \quad (x,y\in \CC) $$ and some sequences of special kind. As an application we solve the equation in the case when $g$ is Jacobi theta function.

functional equation, Weierstrass sigma function, Jacobi theta function, addition formula, elliptic functions, nonlinear sequences

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