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arXiv · 0905.1343

A modular type formula for Euler infinite product $(1-x)(1-xq)(1-xq^2)(1-xq^3)...$

Changgui Zhang
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Abstract

The main goal of this paper is to give a modular type representation for the infinite product $(1-x)(1-xq)(1-xq^2)(1-xq^3)...$. It is shown that this representation essentially contains the well-known modular formulae either for Dedekind's eta function, Jacobi theta function or for certain Lambert series. Thus a new and unified approach is outlined for the study of elliptic and modular functions and related series.

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Changgui Zhang. 2009-05-08. A modular type formula for Euler infinite product $(1-x)(1-xq)(1-xq^2)(1-xq^3)...$. https://arxiv.org/abs/0905.1343

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