Extension of the Kibble-Slepian formula for Hermite polynomials using boson operator methods

DOI10.1016/0196-8858(81)90005-1zbMath0475.33005OpenAlexW2074005716MaRDI QIDQ1159797

James D. Louck

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1016/0196-8858(81)90005-1

zbMATH Keywords

Hermite polynomialsMehler's formulaoperational formula

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items

Multivariate holomorphic Hermite polynomials ⋮ Kibble-Slepian formula and generating functions for 2D polynomials ⋮ The combinatorics of q-Hermite polynomials and the Askey-Wilson integral ⋮ A review of multivariate orthogonal polynomials ⋮ Some Hermite polynomial identities and their combinatorics ⋮ Dual of 2D fractional Fourier transform associated to Itô-Hermite polynomials ⋮ Combinatorial and analytic properties of the \(n\)-dimensional Hermite polynomials ⋮ On the Mehler formula for Hermite polynomials ⋮ A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials ⋮ A tribute to Dennis Stanton ⋮ Analytic properties of complex Hermite polynomials ⋮ Operational rules and arbitrary order Hermite generating functions

Cites Work

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• Invariant theory, Young bitableaux, and combinatorics
• Some extensions of the Mehler formula
• On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory
• On the Symmetrized Kronecker Power of a Matrix and Extensions of Mehler’s Formula for Hermite Polynomials
• On the Representations of the Rotation Group

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