Projection formulas for orthogonal polynomials of a discrete variable

DOI10.1016/0022-247X(74)90131-0zbMath0276.33026MaRDI QIDQ1393648

George Gasper

Publication date: 1974

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) General harmonic expansions, frames (42C15) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (20)

Coefficients of multiplication formulas for classical orthogonal polynomials ⋮ Orthogonal Polynomials in Two Variables of q-Hahn and q-Jacobi Type ⋮ Connection and inversion coefficients for basic hypergeometric polynomials ⋮ Corrigendum: Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Discrete case ⋮ Representations of orthogonal polynomials ⋮ Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials ⋮ Extensions to generalizations of hypergeometric and basic hypergeometric functions of inequalities for quotients of hypergeometric functions that arose in research on financing efficiency of securities-based crowdfunding ⋮ The power collection method for connection relations: Meixner polynomials ⋮ Inversion problems in the \(q\)-Hahn tableau ⋮ On the connection and linearization problem for discrete hypergeometric \(q\)-polynomials ⋮ Connection coefficients between Boas--Buck polynomial sets ⋮ Some properties of polynomials orthogonal over the set \(\langle1,2,\rangle\) ⋮ Solving connection and linearization problems within the Askey scheme and its \(q\)-analogue via inversion formulas ⋮ Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable ⋮ Stochastic processes and special functions: On the probabilistic origin of some positive kernels associate with classical orthogonal polynomials ⋮ Recurrences and explicit formulae for the expansion and connection coefficients in series of classical discrete orthogonal polynomials ⋮ Nonnegativity of a discrete Poisson kernel for the Hahn polynomials ⋮ Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice ⋮ Connection problems for polynomial solutions of nonhomogeneous differential and difference equations ⋮ Recurrence relation approach for expansion and connection coefficients in series of Hahn polynomials

Cites Work

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• Integral representations for Jacobi polynomials and some applications
• Nonnegativity of a discrete Poisson kernel for the Hahn polynomials
• On the positivity of certain sums of ultraspherical polynomials
• Summability of Jacobi Series
• Jacobi polynomial expansions with positive coefficients and imbeddings of projective spaces
• An Integral Representation and Some Summation Formulas for the Hahn Polynomials
• The Generating Function of Jacobi Polynomials

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