The Laguerre-Sobolev-type orthogonal polynomials. Holonomic equation and electrostatic interpretation

DOI10.1216/RMJ-2011-41-1-95zbMath1214.33007OpenAlexW2090594335MaRDI QIDQ627374

Francisco Marcellán, Herbert Dueñas

Publication date: 1 March 2011

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-2011-41-1-95

zbMATH Keywords

orthogonal polynomialszerosLaguerre polynomialslogarithmic potentialholonomic equation

Mathematics Subject Classification ID

Other special orthogonal polynomials and functions (33C47)

Related Items (8)

Asymptotics for Laguerre-Sobolev type orthogonal polynomials modified within their oscillatory regime ⋮ Asymptotic properties of Laguerre-Sobolev type orthogonal polynomials ⋮ Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case ⋮ Characterizations of distributional weights for weak orthogonal polynomials satisfying a second-order differential equation ⋮ Sobolev orthogonal polynomials of several variables on product domains ⋮ Jacobi–Sobolev-type orthogonal polynomials: holonomic equation and electrostatic interpretation – a non-diagonal case ⋮ Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives ⋮ ON LAGUERRE–SOBOLEV TYPE ORTHOGONAL POLYNOMIALS: ZEROS AND ELECTROSTATIC INTERPRETATION

Cites Work

• Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports
• On the assignment of a Dirac-mass for a regular and semi-classical form
• Variations on a theme of Heine and Stieltjes: An electrostatic interpretation of the zeros of certain polynomials
• Classical orthogonal polynomials: A functional approach
• Quasi-orthogonality with applications to some families of classical orthogonal polynomials.
• Asymptotic properties of generalized Laguerre orthogonal polynomials.
• On Sobolev orthogonality for the generalized Laguerre polynomials
• Electrostatic models for zeros of polynomials: old, new, and some open problems
• On Orthogonal Polynomials of Sobolev Type: Algebraic Properties and Zeros
• More on Electrostatic Models for Zeros of Orthagonal Polynomials
• A Generalization of Laguerre Polynomials
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