Some Applications of Celebrated Master Theorem of Ramanujan

IfF(x)is expanded in the form of Maclaurin’s seriesF(x) =∞∑n=0{(−1)ndnF(x)dxn}x=0(−x)nn!then Ramanujan asserts that the value ofI=∫∞0xs−1F(x) dxcan be found from the coefficientof(−x)nn!in the expansion ofF(x). Conversely Ramanujan claims that if the value ofIis known,then the Maclaurin’s coefficient ofF(x)can be found.In this paper, we obtain Maclaurin’s expansions and Mellin transforms of some composite functions,usingRamanujan’s Master theorem