Asymptotic expansion of the modified Lommel polynomials $h_{n,\nu }(x)$ and their zeros

DOI10.1090/S0002-9939-2014-12134-4zbMath1298.41046MaRDI QIDQ3190398

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Publication date: 17 September 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Airy functionuniform asymptotic expansionsmodified Lommel polynomialssecond-order linear difference equations

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Additive difference equations (39A10)

Related Items (2)

The asymptotic zero distribution of Lommel polynomials as functions of their order with a variable complex argument ⋮ Recurrence relations for the moments of discrete semiclassical functionals of class s≤2

Cites Work

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• The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
• Asymptotic expansions for second-order linear difference equations with a turning point
• Uniform asymptotic expansion of \(J_\nu(\nu a)\) via a difference equation
• On Lommel and Bessel Polynomials

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