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Research Article Open access CC BY 3.0

Some Applications of Celebrated Master Theorem of Ramanujan

M. I. Qureshi, Kaleem A. Quraishi, Ram Pal

Journal of Advances in Mathematics and Computer Science · pp. 2862–2871 · Published 27 Jul 2014

10.9734/BJMCS/2014/4842

Abstract

If F(x) is expanded in the form of Maclaurin’s series then Ramanujan asserts that the value of can be found from the coefficient of  in the expansion of F(x). Conversely Ramanujan claims that if the value of I is known, then the Maclaurin’s coefficient of F(x) can be found. In this paper, we obtain Maclaurin’s expansions and Mellin transforms of some composite functions, using Ramanujan’s Master theorem.

Ramanujan Master Theorem Gauss hypergeometric function Pochhammer’s symbol Legendre’s duplication formula Mellin transform Inverse Mellin transform Maclaurin’s expansion Beta and Gamma functions.

Cited by 1

Generalizations and applications of Srinivasa Ramanujan’s integral associated with infinite Fourier sine transforms in terms of Meijer’s G-function

Mohammad Idris Qureshi, Showkat Ahmad Dar · Analysis · 2021

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