A Generalization of Zwegers' -Function According to the -Hermite-Weber Difference Equation

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Authors: Shibukawa, Genki, Tsuchimi, Satoshi
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211870
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Generalization of Zwegers' -Function According to the -Hermite-Weber Difference Equation. Genki Shibukawa and Satoshi Tsuchimi. SIGMA 19 (2023), 014, 23 pages

We introduce a one-parameter deformation of the Zwegers' -function as the image of -Borel and -Laplace transformations of a fundamental solution for the -Hermite-Weber equation. We further give some formulas for our generalized -function, for example, forward and backward shift, translation, sy...