A note on a generalized circular summation formula of theta functions
Jun-Ming Zhu
TL;DR
This paper corrects a previous formula related to theta functions and introduces new transformation formulas for generalized cubic theta functions, enhancing the mathematical understanding of these functions.
Contribution
It provides corrected and generalized imaginary transformation formulas for theta functions, expanding the theoretical framework.
Findings
Corrected the imaginary transformation formula of Chan and Liu's circular theta functions
Derived new transformation formulas for generalized cubic theta functions
Improves the theoretical understanding of theta function transformations
Abstract
In this note, we make a correction of the imaginary transformation formula of Chan and Liu's circular formula of theta functions. We also get the imaginary transformation formulaes for a type of generalized cubic theta functions.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Mathematical Inequalities and Applications