A Generalization of Zwegers' -Function According to the -Hermite-Weber Difference Equation
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211870 |
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| 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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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, symmetry, a difference equation for the new parameter, and bilateral -hypergeometric expressions. From one point of view, the continuous -Hermite polynomials are some special cases of our -function, and the Zwegers' -function is regarded as a continuous -Hermite polynomial of ''−1 degree''.
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| ISSN: | 1815-0659 |