Omprakash Atale

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math.GM2024

Functional equation for Mellin transform of Fourier series associated with modular forms

Omprakash Atale

Let $X_{1} (s)$ and $X_{2} (s)$ denote the Mellin transforms of $I ¨ _{1} (x)$ and $I ¨ _{2} (x)$ , respectively. Ramanujan investigated the functions $I ¨ _{1} (x)$ and $I ¨ _{2} (x)$ that satisfy the f…

math.GM2024

On Finite Mellin Transform via Ramanujan's Master Theorem

Omprakash Atale

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 tran…