Derivatives of any order of the hypergeometric function pFq(a1,...,ap; b1,..., bq; z) with respect to the parameters ai and bi

The derivatives of any order of the general hypergeometric function F-p(q)(a(1),..., a(p); b(1),..., b(q); z) with respect to the parameters a(i) or b(i) are expressed, in compact form, in terms of generalizations of multivariable Kampe de Feriet functions. To achieve this, use is made of Babister's solution to non-homogeneous differential equations for F-p(q)(a(1),..., a(p); b(1),..., b(q); z). An application to Hahn polynomials, which are F-3(2) functions, is given as an illustration.