Linearization and connection formulae involving squares of Gegenbauer polynomials

DOI10.1016/S0893-9659(00)00146-4zbMath0978.33003OpenAlexW2057530701MaRDI QIDQ5938912

Jorge Sánchez-Ruiz

Publication date: 7 August 2001

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(00)00146-4

zbMATH Keywords

orthogonal polynomialshypergeometric polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (14)

Expansions in series of varying Laguerre polynomials and some applications to molecular potentials ⋮ New formulas for the linearization coefficients of some nonsymmetric Jacobi polynomials ⋮ Information-theoretic measures of hyperspherical harmonics ⋮ Linearization coefficients of some particular Jacobi polynomials via hypergeometric functions ⋮ New linearization formulae for the products of Chebyshev polynomials of third and fourth kinds ⋮ Linearization formulae for certain Jacobi polynomials ⋮ Weighted \(L^2\)-norms of Gegenbauer polynomials ⋮ Certain classes of polynomial expansions and multiplication formulas. ⋮ Linearization and Krein-like functionals of hypergeometric orthogonal polynomials ⋮ Unnamed Item ⋮ New formulae between Jacobi polynomials and some fractional Jacobi functions generalizing some connection formulae ⋮ Some connection and linearization problems for polynomials in and beyond the Askey scheme ⋮ Lupaş-type inequality and applications to Markov-type inequalities in weighted Sobolev spaces ⋮ New product and linearization formulae of Jacobi polynomials of certain parameters

Cites Work

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• Operational rules and arbitrary order Hermite generating functions
• Linearization and connection coefficients for hypergeometric-type polynomials
• New identities for orthogonal polynomials on a compact interval
• Information entropy of classical orthogonal polynomials and their application to the harmonic oscillator and Coulomb potentials
• Representations of orthogonal polynomials
• Expansions in series of orthogonal hypergeometric polynomials
• Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials
• The special functions and their approximations. Vol. I, II
• Expansions of Hypergeometric Functions in Hypergeometric Functions
• Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator eigenstates
• General linearization formulae for products of continuous hypergeometric-type polynomials

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