ORTHOGONALITY-PRESERVING LOWERING DIFFERENTIAL OPERATOR FOR LAGUERRE AND JACOBI POLYNOMIALS
Abstract
We describe all Λc-classical orthogonal polynomials, where Λc, c∈ℂ is a fourth-order lowering differential operator. The solutions are the Laguerre {Ln(3)}n≥0 and the Jacobi {Pn(α−4,3)}n≥0. As an illustration, some connection formulas between the polynomial solutions are deduced.
Fields of Study & Subjects
Mathematical functions and polynomials
Mathematical Analysis and Transform Methods
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Rocky Mountain Journal of Mathematics
- Volume
- 56
- Issue
- 1
- Pages
- 237–249
- Publication date
- 1 February 2026