On Finite Mellin Transform via Ramanujan's Master Theorem
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866912020867055616 |
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| author | Atale, Omprakash |
| author_facet | Atale, Omprakash |
| contents | This paper aims to show that by making use of Ramanujan's Master Theorem and the properties of the lower incomplete gamma function, it is possible to construct a finite Mellin transform for the function $f(x)$ that has infinite series expansions in positive integral powers of $x$. Some applications are discussed by evaluating certain definite integrals. The obtained solutions are also compared with results from Mathematica to test the validity of the calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Finite Mellin Transform via Ramanujan's Master Theorem Atale, Omprakash General Mathematics This paper aims to show that by making use of Ramanujan's Master Theorem and the properties of the lower incomplete gamma function, it is possible to construct a finite Mellin transform for the function $f(x)$ that has infinite series expansions in positive integral powers of $x$. Some applications are discussed by evaluating certain definite integrals. The obtained solutions are also compared with results from Mathematica to test the validity of the calculations. |
| title | On Finite Mellin Transform via Ramanujan's Master Theorem |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2409.06304 |