On the functional equation for classical orthogonal polynomials on lattices
K. Castillo, D. Mbouna, J. Petronilho
TL;DR
This paper establishes conditions for solutions of the functional equation related to classical orthogonal polynomials on lattices, providing formulas for Rodrigues and recurrence coefficients.
Contribution
It presents necessary and sufficient conditions for the regularity of solutions and derives explicit formulas for Rodrigues and recurrence coefficients.
Findings
Conditions for regular solutions are characterized.
Explicit Rodrigues formula is provided.
Closed-form recurrence coefficients are derived.
Abstract
Necessary and sufficient conditions for the regularity of solutions of the functional equation appearing in the theory of classical orthogonal polynomials on lattices are stated. Moreover, the functional Rodrigues formula and a closed formula for the recurrence coefficients are presented.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFunctional Equations Stability Results · Mathematical functions and polynomials · Scientific Measurement and Uncertainty Evaluation