$q$-Classical orthogonal polynomials: A general difference calculus approach
, 2009 It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator.
A.F. Nikiforov +26 more
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Fast Computation of Hahn Polynomials for High Order Moments
, 2021 Basheera M. Mahmmod +3 more
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The role of orthogonal polynomials in the six-vertex model and its combinatorial applications
, 2006 The Hankel determinant representations for the partition function and boundary correlation functions of the six-vertex model with domain wall boundary conditions are investigated by the methods of orthogonal polynomial theory.
A G Pronko +24 more
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Bispectral dual Hahn polynomials with an arbitrary number of continuous parameters [PDF]
Journal of Approximation Theory, 2021 Antonio J. Durán Guardeño
semanticscholar +1 more source
Properties of some families of hypergeometric orthogonal polynomials in several variables
, 1996 Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables consisting of ...
van Diejen, Jan F.
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Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials [PDF]
, 2023 Amílcar Branquinho +3 more
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Multidimensional Hahn polynomials, intertwining functions on the\n symmetric group and Clebsch-Gordan coefficients [PDF]
, 2008 Fabio Scarabotti
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Integral Representations of the Wilson Polynomials and the Continuous Dual Hahn Polynomials
Advances in Applied Mathematics, 1999 Let \(\{p_n(x)\}_{n=0,1, \dots}\) denote the set of monic orthogonal polynomials, \(p_n(x)\) of degree \(n\), associated with the weight function \(w(x)\). Then it is straightforward to show \[ p_n(x)={1\over C} \int^\infty_{-\infty} dx_1w(x_1) \dots\int^\infty_{- \infty} dx_Nw(x_N) \prod^N_{l=1} (x-x_1) \prod_{1\leq ...
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An Orthogonal Polynomial Solution to the Confluent-Type Heun’s Differential Equation
MathematicsIn this work, we present both analytical and numerical solutions to a seven-parameter confluent Heun-type differential equation. This second-order linear differential equation features three singularities: two regular singularities and one irregular ...
Saiful R. Mondal, Varun Kumar
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Quadratic decomposition of a Laguerre-Hahn polynomial sequence I
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2010 Let \(P_n\) and \(B_n\) be sequences of monic orthogonal polynomials such that \(B_{2n}(x)=P_n(x^2)\) for all \(n\geq0\). In the present paper, the authors prove that, if one of the sequences is a Laguerre-Hahn orthogonal polynomial sequence, then so is the other.
Bouras, B., Marcellan, F.
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