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

L. U. ANCARANI AND G. GASANEO

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Año: 2009 vol. 42 p. 1 - 10

1751-8113

Abstract The derivatives to any order of the Gaussian hypergeometric function 2 F1 (a, b, c; z) with respect to the parameters a, b and c are expressed in terms of generalizations of multivariable Kamp ́ de F ́ riet functions. Several e e 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.