Derivatives of any order of the Gaussian hypergeometric function 2F1(a, b, c; z) with respect to the parameters a, b and c

The derivatives to any order of the Gaussian hypergeometric function F-2(1) (a, b, c; z) with respect to the parameters a, b and c are expressed in terms of generalizations of multivariable Kampe de Feriet functions. Several properties are presented. In an application to the two-body Coulomb scattering problem, the usefulness of these derivatives is illustrated with the study of the charge dependence of Pollaczek-like polynomials.