Gauss’s binomial formula and additive property of exponential functions on T(q,h)

In this article, we focus our attention on (q,h)-Gauss?s binomial formula from which discover the additive property of (q; h)-exponential functions. We state (q,h)-analogue Gauss?s in terms proper polynomials T(q,h) own essential properties similar to ordinary polynomials. present (q,h)-Taylor series and analyze conditions for its convergence. introduce a new (q,h)-analytic exponential function admits property. As consequences, study (q,h)-hyperbolic functions, (q,h)-trigonometric functions their significant such as (q,h)-Pythagorean Theorem double-angle formulas. Finally, illustrate results by first order (q,h)-difference equation, (q,h)-analogues dynamic diffusion equation Burger?s equation. Introducing (q,h)-Hopf-Cole transformation, obtain (q,h)-shock soliton solutions