Results 11 to 20 of about 1,874,459 (287)
Computation of Fourier transform representations involving the generalized Bessel matrix polynomials
Advances in Difference Equations, 2021 Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive the formulas for Fourier cosine and sine transforms of ...
M. Abdalla, M. Akel
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Laguerre–Freud Equations for the Gauss Hypergeometric Discrete Orthogonal Polynomials
Mathematics, 2023 The Cholesky factorization of the moment matrix is considered for the Gauss hypergeometric discrete orthogonal polynomials. This family of discrete orthogonal polynomials has a weight with first moment given by ρ0=2F1a,bc+1;η.
Itsaso Fernández-Irisarri +1 more
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Asymptotics of matrix valued orthogonal polynomials on [−1,1]
Advances in Mathematics, 2023 We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and a matrix part. Using the Riemann-Hilbert formulation for MVOPs and the Deift-Zhou method of steepest descent, we obtain asymptotic expansions for the MVOPs as the degree tends to infinity, in ...
Deano, Alfredo +2 more
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On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials
Mathematics, 2020 The generalization of Rodrigues’ formula for orthogonal matrix polynomials has attracted the attention of many researchers. This generalization provides new integral and differential representations in addition to new mathematical results that are ...
Mohra Zayed +3 more
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Matrix polynomials orthogonal with respect to a non-symmetric matrix of measures [PDF]
Opuscula Mathematica, 2016 The paper focuses on matrix-valued polynomials satisfying a three-term recurrence relation with constant matrix coefficients. It is shown that they form an orthogonal system with respect to a matrix of measures, not necessarily symmetric. Moreover, it is
Marcin J. Zygmunt
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Mathematics, 2015 The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
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Matrix biorthogonal polynomials on the real line: Geronimus transformations [PDF]
Bulletin of Mathematical Sciences, 2019 In this paper, Geronimus transformations for matrix orthogonal polynomials in the real line are studied. The orthogonality is understood in a broad sense, and is given in terms of a nondegenerate continuous sesquilinear form, which in turn is determined ...
Gerardo Ariznabarreta +3 more
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Orthogonal Polynomials On Ellipses And Their Recurrence Relations
Demonstratio Mathematica, 2014 In this note we study the connection between orthogonal polynomials on an ellipse and orthogonal Laurent polynomials on the unit circle relative to some multiplicative measures and then establish the recurrence relations for orthogonal polynomials on an ...
Lauric Vasile
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The Matrix Ansatz, orthogonal polynomials, and permutations
Advances in Applied Mathematics, 2011 In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We illustrate this approach with applications to moments of orthogonal polynomials, permutations, signed permutations,
Corteel, Sylvie +2 more
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Characteristic polynomials of complex random matrix models [PDF]
, 2002 We calculate the expectation value of an arbitrary product of characteristic polynomials of complex random matrices and their hermitian conjugates. Using the technique of orthogonal polynomials in the complex plane our result can be written in terms of
Akemann, G +3 more
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