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

Robin, William

Abstract

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].

Citation

Robin, W. (2013). On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation. International Mathematical Forum, 8, 1455-1466. https://doi.org/10.12988/imf.2013.37133

• 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
• DOI: https://doi.org/10.12988/imf.2013.37133
• Keywords: hypergeometric-type differential equation; Rodrigues formula; generalized Rodrigues formula; integration technique
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/7778
• Publisher URL: http://dx.doi.org/10.12988/imf.2013.37133