Generalizations of Rodrigues type formulas for hypergeometric difference equations on nonuniform lattices

By building a second-order adjoint difference equations on nonuniform lattices, the generalized Rodrigues type representation for the second kind solution of a second-order difference equation of hypergeometric type on nonuniform lattices is given. The general solution of the equation in the form of...

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Bibliographic Details
Published in:Journal of difference equations and applications 2020-04, Vol.26 (4), p.435-457
Main Authors: Cheng, Jinfa, Jia, Lukun
Format: Article
Language:English
Subjects:
adjoint difference equation
difference equation of hypergeometric type
Difference equations
Formulas (mathematics)
Lattices (mathematics)
Mathematical analysis
nonuniform lattice
orthogonal polynomials
Special function
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Summary:By building a second-order adjoint difference equations on nonuniform lattices, the generalized Rodrigues type representation for the second kind solution of a second-order difference equation of hypergeometric type on nonuniform lattices is given. The general solution of the equation in the form of a combination of a standard Rodrigues formula and a 'generalized' Rodrigues formula is also established.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2020.1748019