Two families of orthogonal polynomials related to Jacobi polynomials

DOI10.1216/rmjm/1181073013zbMath0744.33004OpenAlexW4229972231MaRDI QIDQ1178592

Mourad E. H. Ismail, David R. Masson

Publication date: 26 June 1992

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

Full work available at URL: https://doi.org/10.1216/rmjm/1181073013

zbMATH Keywords

associated Jacobi polynomialweight functiongenerating functionrecurrence relationJacobi polynomialsasymptotic results

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (8)

Co-recursive associated Jacobi polynomials ⋮ Computation of limit periodic continued fractions. A survey ⋮ Asymptotic behavior of solutions of three-term Poincaré difference equations ⋮ The bilateral birth–death chain generated by the associated Jacobi polynomials ⋮ Recursive three-term recurrence relations for the Jacobi polynomials on a triangle ⋮ Beta Jacobi ensembles and associated Jacobi polynomials ⋮ The Associated Askey-Wilson Polynomials ⋮ The classical β-ensembles with β proportional to 1/N: From loop equations to Dyson’s disordered chain

Cites Work

• Linear birth and death models and associated Laguerre and Meixner polynomials
• Bernstein's inequality in \(L^p\) for \(O<p<1\)
• Quadratic Birth and Death Processes and Associated Continuous Dual Hahn Polynomials
• The rotating harmonic oscillator eigenvalue problem. I. Continued fractions and analytic continuation
• Associated Laguerre and Hermite polynomials
• Recurrence relations, continued fractions, and orthogonal polynomials
• Explicit Formulas for the Associated Jacobi Polynomials and Some Applications
• Ramanujan's Extensions of the Gamma and Beta Functions
• The Associated Ultraspherical Polynomials and their _q-Analogues
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