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arXiv · 1712.06097

Finite and infinite product transformations

Martin Nicholson
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Abstract

Several infinite products are studied that satisfy the transformation relation of the type $f(\alpha)=f(1/\alpha)$. For certain values of the parameters these infinite products reduce to modular forms. Finite counterparts of these infinite products are motivated by solution of Dirichlet boundary problem on a rectangular grid. These finite product formulas give an elementary proof of several modular transformations.

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Martin Nicholson. 2017-12-17. Finite and infinite product transformations. https://arxiv.org/abs/1712.06097

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