In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler's theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside's series. A Semi-Taylor series is introduced as the special case of the Taylor-Riemann series when \alpha=1/2, and some of its relations to special functions are obtained via certain generating functions arising in complex fractional calculus.
Andreas Strömbergsson, Department of Mathematics, Uppsala University, Sweden email@example.com
"Fractional Calculus and the Taylor-Riemann Series,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 6
, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol6/iss1/6