Finding all hypergeometric solutions of linear differential equations
Marko Petkovšek, Bruno Salvy · 1993
Hypergeometric sequences are such that the quotient of two successive terms is a fixed rational function of the index. We give a generalization of M. Petkovsek's algorithm to find all hypergeometric sequence solutions of linear recurrences, and we describe a program to find all hypergeometric functions that solve a linear differential equation. Solutions hyperg'eom'etriques des 'equations diff'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 fixe de l'indice. Nous donnons une g'en'eralisation de l'algorithme de M. Petkovsek qui d'etermine toutes les solutions hyperg'eom'etriques de r'ecurrences lin'eaires, et nous d'ecrivons un programme qui donne toutes les fonctions hyperg'eom'etriques solutions d"equations diff'erentielles lin'eaires. To appear in Proceedings ISSAC'93. M. Bronstein ed. ACM Press. Finding All Hypergeometric Solutions of Linear Differential Equations Marko Petkovsek ...