Power function and binomial series on T _{( q , h )}

This 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.