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On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation

Robin, William


William Robin


In this paper, we present a new systematic approach to the solution of the hypergeometric-like differential equation and its associated equation. The method produces, tout court, the general solution of these equations in the form of a combination of a standard Rodrigues formula and a ‘generalized’ Rodrigues formula, of a type due originally to Gonçalves [5] and recently considered, again, by Area et al [1]. In addition, a novel analysis of a class of integrals determining the generalized Rodrigues formulae is given, which complements an original analysis of Area et al [1]. Finally, the relation between the hypergeometric-type differential equation and the hypergeometric equation is elucidated further, following the work of Koepf and Masjed-Jamel [7].


Robin, W. (2013). On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation. International Mathematical Forum, 8, 1455-1466.

Journal Article Type Article
Publication Date 2013
Deposit Date Apr 22, 2015
Publicly Available Date Apr 22, 2015
Electronic ISSN 1312-7594
Publisher Hikari
Peer Reviewed Peer Reviewed
Volume 8
Pages 1455-1466
Keywords hypergeometric-type differential equation; Rodrigues formula; generalized Rodrigues formula; integration technique
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