Several special values of Jacobi theta functions
Istv\'an Mez\H{o}
TL;DR
This paper derives new special values for the first two Jacobi theta functions using elliptic function duplication formulas and explores their connections with Weber modular functions.
Contribution
It introduces novel special values for Jacobi theta functions and demonstrates methods to extend these results to a broader class of identities.
Findings
New special values for Jacobi theta functions derived
Established connections between theta functions and Weber modular function
Methodology for extending special value derivations
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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Taxonomy
TopicsAdvanced Mathematical Identities · Molecular spectroscopy and chirality · Advanced Combinatorial Mathematics