Differential Formulas for q-Integral Representation of (τ, β)-Generalized Hypergeometric Function.

The key objective of this paper is to obtain differential formulas for q-integral representation of (τ, β)-generalized hypergeometric function. To this end, we consider new (τ, β)-generalized hypergeometric functions Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. Using the integral property of q-beta function for the function Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed, we obtain the q-integral representation. Employing the body of the theory of fractional differentiation, we also investigate a series of q-differential relations for these new generalized hypergeometric functions. The results obtained allow widely applying Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed functions to solve problems of mathematical physics, differential and integral equations, the theory of probability, mathematical statistics and others. [ABSTRACT FROM AUTHOR]