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arXiv · 2105.12947

On certain extensions of Ramanujan's Master Theorem and their applications

Omprakash Atale·Mahendra Shirude
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Abstract

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.

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Omprakash Atale, Mahendra Shirude. 2021-05-27. On certain extensions of Ramanujan's Master Theorem and their applications. https://arxiv.org/abs/2105.12947

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