Seçil GergünBurcu SilindirAhmet Yantir2025-10-062023276909112769-091110.1080/27690911.2023.2168657https://www.scopus.com/inward/record.uri?eid=2-s2.0-85148540655&doi=10.1080%2F27690911.2023.2168657&partnerID=40&md5=d5e43eba090ced08c9aaff1577feeb66https://gcris.yasar.edu.tr/handle/123456789/8582This 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.English-analytic Functions, Gauss' Binomial Formula, Nabla -binomial Series, Nabla -power Function, Nabla Generalized Quantum Binomial, Newton's Binomial Formula, -analytic Function, Additivity, Analytic Functions, Binomial Series, Gauss' Binomial Formula, Nablum -binomial Series, Nablum -power Function, Nablum Generalized Quantum Binomial, Newton Binomial Formula, Power Functions, Functional Analysis-analytic function, Additivity, Analytic functions, Binomial series, Gauss' binomial formula, Nablum -binomial series, Nablum -power function, Nablum generalized quantum binomial, Newton binomial formula, Power functions, Functional analysisArticle