Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation [PDF]
Studies in applied mathematics (Cambridge)This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi–Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials.
Amílcar Branquinho +3 more
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Classical Orthogonal Polynomials as Moments [PDF]
Canadian Journal of Mathematics, 1997 AbstractWe show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous q-ultraspherical polynomials and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures.We use this fact to derive bilinear and multilinear generating functions for some of these polynomials.
Mourad E. H. Ismail, Dennis Stanton
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Orthogonal Polynomials With a Semi-Classical Weight and Their Recurrence Coefficients [PDF]
IEEE Access, 2020 Focusing on the weight function $\omega (x,t)=x^{\alpha }e^{-\frac {1}{3}x^{3}+tx}, x\in [0,\infty),\,\,\,\,\alpha >-1,\,\,\,\,t> 0$ , we state its asymptotic orthogonal polynomials.
Dan Wang, Mengkun Zhu, Yang Chen
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Discriminants of classical quasi-orthogonal polynomials with application to Diophantine equations [PDF]
Journal of the Mathematical Society of Japan, 2019 We derive explicit formulas for the discriminants of classical quasi-orthogonal polynomials, as a full generalization of the result of Dilcher and Stolarsky (2005).
Masanori Sawa, Yukihiro Uchida
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Algorithms for classical orthogonal polynomials [PDF]
, 1996 In this article explicit formulas for the recurrence equation p_{n+1}(x) = (A_n x + B_n) p_n(x) - C_n p_{n-1}(x) and the derivative rules sigma(x) p'_n(x) = alpha_n p_{n+1}(x) + beta_n p_n(x) + gamma_n p_{n-1}(x) and sigma(x) p'_n(x) = (alpha_n-tilde x + beta_n-tilde) p_n(x) + gamma_n-tilde p_{n-1}(x) respectively which are valid for the orthogonal ...
Wolfram Koepf, Dieter Schmersau
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On ( p , q ) $(p,q)$ -classical orthogonal polynomials and their characterization theorems
Advances in Difference Equations, 2017 In this paper, we introduce a general ( p , q ) $(p, q)$ -Sturm-Liouville difference equation whose solutions are ( p , q ) $(p, q)$ -analogues of classical orthogonal polynomials leading to Jacobi, Laguerre, and Hermite polynomials as ( p , q ) → ( 1 ...
M Masjed-Jamei +3 more
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Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions [PDF]
Transactions of the American Mathematical Society, 2019 The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalized to discrete settings involving either a linear or an exponential lattice. The corresponding correlation functions can be expressed in terms of
Peter J. Forrester, Shi‐Hao Li
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Explicit barycentric formulae for osculatory interpolation at roots of classical orthogonal polynomials [PDF]
Mathematics of Computation, 2016 Przemysław Rutka, Ryszard Smarzewski
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Connection coefficients for classical orthogonal polynomials of several variables [PDF]
, 2017 Plamen Iliev, Yuan Xu
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Elektronika ir Elektrotechnika, 2022 This paper presents one possible application of generalized quasi-orthogonal functional networks in the sensitivity analysis of complex dynamical systems.
Sasa S. Nikolic +6 more
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