Some Infinite Series and Functional Relations That Arose in the Context of Fractional Calculus

Several interesting infinite series relations were derived recently by applying such operators of fractional calculus as the familiar Riemann–Liouville fractional differintegral operator 0Dμ z of (real or complex) order μ.The main object of this paper is to present much simpler alternative derivations of substantially more general families of infinite series relations without using fractional calculus.Some relevant connections among various known results are also provided