Finding All Hypergeometric Solutions of Linear Diierential Equations Finding All Hypergeometric Solutions of Linear Diierential Equations Finding All Hypergeometric Solutions of Linear Diierential Equations

Hypergeometric sequences are such that the quotient of two successive terms is a xed rational function of the index. We give a generalization of M. Petkov sek's algorithm to nd all hypergeometric sequence solutions of linear recurrences, and we describe a program to nd all hypergeometric functions that solve a linear diierential equation. Solutions hyperg eom etriques des equations dii erentielles lin eaires R esum e Les suites hyperg eom etriques sont telles que le quotient de deux termes cons ecutifs est une fonction rationnelle xe de l'indice. Nous donnons une g en eralisation de l'algorithme de M. Petkov sek qui d etermine toutes les solutions hyperg eom etriques de r ecurrences lin e-aires, et nous d ecrivons un programme qui donne toutes les fonctions hyperg eom etriques solutions d' equations dii erentielles lin eaires. Abstract Hypergeometric sequences are such that the quotient of two successive terms is a xed rational function of the index. We give a generalization of M. Petkov sek's algorithm to nd all hypergeometric sequence solutions of linear recurrences, and we describe a program to nd all hypergeometric functions that solve a linear diierential equation.