On the connection coefficients and recurrence relations arising from expansions in series of hermite polynomials

DOI10.1080/10652460310001600618zbMath1040.42020OpenAlexW2009615979MaRDI QIDQ4470650

Eid H. Doha

Publication date: 15 June 2004

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460310001600618

zbMATH Keywords

Chebyshev polynomialsHermite polynomialsrecurrence relationsconnection coefficientsHermite expansion coefficientsLaguerre-Hermite polynomialsJacobi-Hermite polynomialsordinary differential equations with varying coefficients

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items

New linearization formulae for the products of Chebyshev polynomials of third and fourth kinds, Linearization formulae for certain Jacobi polynomials, Linearization coefficients for Boas-Buck polynomial sets, Unnamed Item, Spectral solutions for differential and integral equations with varying coefficients using classical orthogonal polynomials, On the neutral Hermite product of the distributionsx^±nand δ^(m)(x), Recurrences and explicit formulae for the expansion and connection coefficients in series of ordinary Bessel polynomials, New formulae between Jacobi polynomials and some fractional Jacobi functions generalizing some connection formulae, The general Jacobi matrix method for solving some nonlinear ordinary differential equations, On the derivatives of Bernstein polynomials: an application for the solution of high even-order differential equations, Explicit formulae for the coefficients of integrated expansions of Laguerre and Hermite polynomials and their integrals, Recurrences and explicit formulae for the expansion and connection coefficients in series of classical discrete orthogonal polynomials, Recurrence relation approach for expansion and connection coefficients in series of Hahn polynomials, On the coefficients of integrated expansions of Bessel polynomials, New product and linearization formulae of Jacobi polynomials of certain parameters

Cites Work

• Unnamed Item
• Unnamed Item
• The coefficients of differentiated expansions and derivatives of ultraspherical polynomials
• A note on the Chebyshev coefficients of the moments of the general order derivative of an infinitely differentiable function
• A note on the Chebyshev coefficients of the general order derivative of an infinitely differentiable function
• Parallelism in spectral methods
• Quick construction of recurrence relations for the Jacobi coefficients
• Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Continuous case
• The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function
• Expansions in series of orthogonal hypergeometric polynomials
• Recurrence relations for connection coefficients between two families of orthogonal polynomials
• The numerical solution of linear recurrence relations
• The special functions and their approximations. Vol. I, II
• On the Legendre Coefficients of a General-Order Derivative of an Infinitely Differentiable Function
• On the coefficients of differentiated expansions and derivatives of Jacobi polynomials
• Efficient Spectral-Galerkin Algorithms for Direct Solution of Second-Order Equations Using Ultraspherical Polynomials
• The first and second kind chebyshev coefficients of the moments for the general order derivative on an infinitely differentiable function
• On the legendre coefficients of the moments of the general order derivative of an infinitely differentiable function
• A modification of Miller's recurrence algorithm