William Robin
On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation
Robin, William
Authors
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 | Mar 29, 2024 |
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 |
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Publisher Licence URL
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