Some Applications of Celebrated Master Theorem of Ramanujan
M. I. Qureshi
Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi-110025, India.
Kaleem A. Quraishi *
Mathematics Section, Mewat Engineering College (Wakf), Palla, Nuh, Mewat-122107, Haryana, India.
Ram Pal
Department of Applied Sciences and Humanities, Aryabhat Polytechnic, G. T. Karnal Road, Delhi-110033, India.
*Author to whom correspondence should be addressed.
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.
Keywords: 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.