Explicit Formulae for the Coefficients of Integrated Expansions of Jacobi Polynomials and Their Integrals

DOI10.1080/10652460304541zbMath1051.33004OpenAlexW1994522942MaRDI QIDQ4409773

Eid H. Doha

Publication date: 30 June 2003

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

Full work available at URL: https://doi.org/10.1080/10652460304541

zbMATH Keywords

Jacobi polynomials

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)

Related Items

Algorithms for construction of recurrence relations for the coefficients of the Fourier series expansions with respect to classical discrete orthogonal polynomials ⋮ Jacobi spectral Galerkin method for the integrated forms of second-order differential equations ⋮ Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations ⋮ Integrals of Chebyshev polynomials of third and fourth kinds: an application to solution of boundary value problems with polynomial coefficients ⋮ Efficient spectral-Petrov-Galerkin methods for the integrated forms of third- and fifth-order elliptic differential equations using general parameters generalized Jacobi polynomials ⋮ Recurrences and explicit formulae for the expansion and connection coefficients in series of ordinary Bessel polynomials ⋮ Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials ⋮ A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations ⋮ Explicit formulae for integro-differential operational matrices ⋮ On Jacobi polynomials \(\mathscr{P}_k^{(\alpha,\beta)}\) and coefficients \(c_j^{\ell}(\alpha,\beta)\) \((k\geq 0, \ell =5,6; 1\leq j\leq \ell; \alpha,\beta > -1)\) ⋮ On Jacobi polynomials and fractional spectral functions on compact symmetric spaces ⋮ A Jacobi spectral Galerkin method for the integrated forms of fourth‐order elliptic differential equations ⋮ Explicit formulae for the coefficients of integrated expansions of Laguerre and Hermite polynomials and their integrals ⋮ Descriptions of fractional coefficients of Jacobi polynomial expansions ⋮ On the coefficients of integrated expansions of Bessel polynomials

Cites Work

• The coefficients of differentiated expansions and derivatives of ultraspherical polynomials
• An accurate solution of parabolic equations by expansion in ultraspherical polynomials
• A note on the Chebyshev coefficients of the general order derivative of an infinitely differentiable function
• Parallelism in spectral methods
• On the coefficients of differentiated expansions of ultraspherical polynomials
• The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
• Gegenbauer approximation and its applications to differential equations on the whole line
• On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations
• An accurate solution of the Poisson equation by the Chebyshev-tau method
• A Chebyshev spectral method for solving Korteweg-de Vries equation with hydrodynamical application
• An Efficient Double Legendre Spectral Method for Parabolic and Elliptic Partial Differential Equations
• On the Coefficients of Integrated Expansions of Ultraspherical Polynomials
• 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
• An efficient spectral method for ordinary differential equations with rational function coefficients
• Unnamed Item
• Unnamed Item
• Unnamed Item