Several special values of Jacobi theta functions

2011/06/14 by István Mező, Mező, István
Mathematics · Chemistry · #Advanced Mathematical Identities #Molecular spectroscopy and chirality #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1106.2703

Abstract

Using the duplication formulas of the elliptic trigonometric functions of Gosper, we deduce some new special values for the first two Jacobi theta functions. At the end of the paper, we show how is it possible to extend our arguments and deduce a wide variety of additional special values for the Jacobi thetas. In addition, an identity is revealed between these functions and the Weber modular function.

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