Two classes of special functions using Fourier transforms of generalized ultraspherical and generalized Hermite polynomials

DOI10.1090/S0002-9939-2011-11063-3zbMath1246.33005MaRDI QIDQ2884426

Wolfram Koepf, Mohammad Masjed-Jamei

Publication date: 29 May 2012

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

zbMATH Keywords

Fourier transformParseval identitygeneralized Hermite polynomialssieved orthogonal polynomialsgeneralized ultraspherical polynmials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (8)

Nontensorial generalised hermite spectral methods for PDEs with fractional Laplacian and Schrödinger operators ⋮ Fourier transforms of some special functions in terms of orthogonal polynomials on the simplex and continuous Hahn polynomials ⋮ Some classes of special functions using Fourier transforms of some two-Variable orthogonal polynomials ⋮ On the orthogonality and convolution orthogonality via the Kontorovich-Lebedev transform ⋮ Two finite classes of orthogonal functions ⋮ A finite class of orthogonal functions generated by Routh–Romanovski polynomials ⋮ An algebraic treatment of the Askey biorthogonal polynomials on the unit circle ⋮ On generating symmetric orthogonal polynomials

Uses Software

• DLMF
• SumTools

Cites Work

• A basic class of symmetric orthogonal polynomials using the extended Sturm-Liouville theorem for symmetric functions
• On sieved orthogonal polynomials. IV. Generating functions
• NIST digital library of mathematical functions
• Sieved Ultraspherical Polynomials
• On Jacobi and continuous Hahn polynomials
• Two classes of special functions using Fourier transforms of some finite classes of classical orthogonal polynomials
• Biorthogonal exponential sequences with weight function $\exp(ax^2+ibx)$ on the real line and an orthogonal sequence of trigonometric functions
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