1 Product formula for the Jacobi theta function
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ar X iv : 0 90 5 . 13 43 v 1 [ m at h . N T ] 8 M ay 2 00 9 A modular type formula for Euler infinite product ( 1 −
The main goal of this paper is to give a modular type representation for the infinite product (1−x)(1−xq)(1−xq)(1−xq) · · · . 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 ...
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In Ramanujan’s final letter to Hardy, he wrote of a strange new class of infinite series he called “mock theta functions”. It turns out all of Ramanujan’s mock theta functions are essentially specializations of a so-called universal mock theta function g3(z, q) of Gordon–McIntosh. Here we show that g3 arises naturally from the reciprocal of the classical Jacobi triple product—and is intimately ...
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