Secil GergunBurcu SilindirAhmet YantirGergün, SeçilSilindir, BurcuYantir, Ahmet2025-10-0620232769-091110.1080/27690911.2023.21686572-s2.0-85148540655http://dx.doi.org/10.1080/27690911.2023.2168657https://gcris.yasar.edu.tr/handle/123456789/6812https://doi.org/10.1080/27690911.2023.2168657This article is devoted to present (q h) -analogue of power function which satisfies additivity and derivative properties similar to the ordinary power function. In the light of nabla (q h) -power function we present (q h)-analogue of binomial series and conclude that such power function is (q h)-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 (q h)-binomial series to classical binomial series Gauss' binomial and Newton's binomial formulas.Englishinfo:eu-repo/semantics/openAccessNabla generalized quantum binomial, nabla (q h)-power function, (q h)-analytic functions, nabla (q h)-binomial series, Newton's binomial formula, Gauss' binomial formulaNabla -Binomial SeriesNabla (q, h)-Binomial Series(Q, h)-Analytic FunctionsNewton’s Binomial FormulaNabla -Power FunctionGauss’ Binomial FormulaNabla Generalized Quantum Binomial-Analytic FunctionsNabla (q, h)-Power FunctionArticle