A note on the Ramanujan master theorem

TL;DR

This paper presents a new integral formula that derives the Ramanujan Master Theorem for positive integers and offers a simple proof for the case when n is not an integer, expanding its theoretical understanding.

Contribution

It introduces a novel integral formula to derive the RMT for positive integers and simplifies the proof for non-integer cases, enhancing theoretical insights.

Findings

Derived RMT from a new integral formula for positive integers

Provided a simple proof of RMT for non-integer n

Expanded understanding of the mathematical foundations of RMT

Abstract

In this note, it is shown that the Ramanujan Master Theorem (RMT) when n is a positive integer can be obtained, as a special case, from a new integral formula. Furthermore, we give a simple proof of the RMT when n is not an integer.