On Fractional derivative of Hurwitz Zeta function and Jacobi Theta function
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916299062378496 |
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| author | Mor, Ashish Gupta, Surbhi Kashyap, Manju |
| author_facet | Mor, Ashish Gupta, Surbhi Kashyap, Manju |
| contents | This research paper focuses on exploring two Complex-valued function's fractional derivative, specifically the Hurwitz Zeta function and Jacobi theta function. The study is based on the Complex Generalization of Grunwald-Letnikov Fractional derivative which adheres to the generalized version of the Leibniz rule. Within this paper, we present and establish an identity that serves as a Generalization of the Hurwitz Zeta function's Functional Equation. Additionally, we derive the Jacobi Theta function's Functional Equation, accompanied by a comprehensive examination of the properties associated with the Fractional derivative of these two functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16942 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Fractional derivative of Hurwitz Zeta function and Jacobi Theta function Mor, Ashish Gupta, Surbhi Kashyap, Manju Classical Analysis and ODEs 26A33, 32A15, 11F27, 11M35, 34K37 This research paper focuses on exploring two Complex-valued function's fractional derivative, specifically the Hurwitz Zeta function and Jacobi theta function. The study is based on the Complex Generalization of Grunwald-Letnikov Fractional derivative which adheres to the generalized version of the Leibniz rule. Within this paper, we present and establish an identity that serves as a Generalization of the Hurwitz Zeta function's Functional Equation. Additionally, we derive the Jacobi Theta function's Functional Equation, accompanied by a comprehensive examination of the properties associated with the Fractional derivative of these two functions. |
| title | On Fractional derivative of Hurwitz Zeta function and Jacobi Theta function |
| topic | Classical Analysis and ODEs 26A33, 32A15, 11F27, 11M35, 34K37 |
| url | https://arxiv.org/abs/2312.16942 |