On certain extensions of Ramanujan's Master Theorem and their applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917634185887744 |
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| author | Atale, Omprakash Shirude, Mahendra |
| author_facet | Atale, Omprakash Shirude, Mahendra |
| contents | S. Ramanujan introduced a technique in 1913 for providing analytic expressions for certain Mellin-type integrals which is now known as Ramanujan's Master Theorem. This technique was communicated through his "Quarterly Reports" and has a wide range of applicability in calculating the values of certain definite integrals. In this paper, we have presented some extensions of Ramanujan's Master Theorem that arise from the k-gamma function and the p-k gamma function. Furthermore, we have established a Mellin type double integral along with its corollaries. Some applications are established through the evaluation of a variety of definite integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_12947 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On certain extensions of Ramanujan's Master Theorem and their applications Atale, Omprakash Shirude, Mahendra Number Theory S. Ramanujan introduced a technique in 1913 for providing analytic expressions for certain Mellin-type integrals which is now known as Ramanujan's Master Theorem. This technique was communicated through his "Quarterly Reports" and has a wide range of applicability in calculating the values of certain definite integrals. In this paper, we have presented some extensions of Ramanujan's Master Theorem that arise from the k-gamma function and the p-k gamma function. Furthermore, we have established a Mellin type double integral along with its corollaries. Some applications are established through the evaluation of a variety of definite integrals. |
| title | On certain extensions of Ramanujan's Master Theorem and their applications |
| topic | Number Theory |
| url | https://arxiv.org/abs/2105.12947 |