Power function and binomial series on

Abstract

This article is devoted to present (Formula presented.) -analogue of power function which satisfies additivity and derivative properties similar to the ordinary power function. In the light of nabla (Formula presented.) -power function we present (Formula presented.) -analogue of binomial series and conclude that such power function is (Formula presented.) -analytic. We prove the analyticity by showing that both the power function and its absolutely convergent Taylor series solve the same IVP. Finally we present the reductions of (Formula presented.) -binomial series to classical binomial series Gauss' binomial and Newton's binomial formulas. © 2023 Elsevier B.V. All rights reserved.