Mixed recurrence equations and interlacing properties for zeros of sequences of classical \(q\)-orthogonal polynomials

DOI10.1016/j.apnum.2017.11.003zbMath1379.65014OpenAlexW2770413954MaRDI QIDQ1686212

Daniel D. Tcheutia, Alta S. Jooste, Wolfram Koepf

Publication date: 21 December 2017

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2017.11.003

zbMATH Keywords

numerical examplesclassical \(q\)-orthogonal polynomialsinterlacing of zerosZeilberger's algorithmmixed recurrence equations

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Numerical aspects of recurrence relations (65Q30)

Related Items (5)

Biorthogonality and para-orthogonality of \(R_I\) polynomials ⋮ Quasi-orthogonality of some hypergeometric and \(q\)-hypergeometric polynomials ⋮ Quasi-orthogonality and zeros of some \({}_2 \phi_2\) and \({}_3 \phi_2\) polynomials ⋮ Interlacing and bounds of zeros of quasi-orthogonal little \(q\)-Jacobi polynomials ⋮ Structure relations of classical orthogonal polynomials in the quadratic and \(q\)-quadratic variable

Uses Software

• SumTools

Cites Work

• Interlacing properties and bounds for zeros of \({}_2\phi_1\) hypergeometric and little \(q\)-Jacobi polynomials
• Mixed recurrence relations and interlacing of the zeros of some \(q\)-orthogonal polynomials from different sequences
• Zeros of generalized Krawtchouk polynomials
• The contiguous function relations for the basic hypergeometric series
• Interlacing of the zeros of Jacobi polynomials with different parameters
• Interlacing theorems for the zeros of some orthogonal polynomials from different sequences
• Compact matrix pseudogroups
• The q-analogue of the Laguerre polynomials
• Quasi-orthogonality with applications to some families of classical orthogonal polynomials.
• A contribution to quasi-orthogonal polynomials and associated polynomials
• Hypergeometric summation. An algorithmic approach to summation and special function identities
• The Differential Equations of Birth-and-Death Processes, and the Stieltjes Moment Problem
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• The Zeros of the Hahn Polynomials
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
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