For mixed multiple orthogonal polynomials, the paper derives Christoffel-type formulas for general Geronimus perturbations and proves that the perturbed orthogonality exists exactly when certain tau-determinants do not vanish.
Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation
1 Pith paper cite this work. Polarity classification is still indexing.
abstract
This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi-Pi\~neiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for nearest-neighbor recurrence coefficients, as well as the step line case, are provided for all these polynomial families. Furthermore, new explicit expressions for type I multiple orthogonal polynomials are derived for Laguerre of the second kind and also for multiple Hermite polynomials.
fields
math.CA 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
General Geronimus Perturbations for Mixed Multiple Orthogonal Polynomials
For mixed multiple orthogonal polynomials, the paper derives Christoffel-type formulas for general Geronimus perturbations and proves that the perturbed orthogonality exists exactly when certain tau-determinants do not vanish.