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Classical 2-orthogonal polynomials and differential equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 We construct the linear differential equations of third order satisfied by the classical 2‐orthogonal polynomials. We show that these differential equations have the following form: , where the coefficients are polynomials whose degrees are, respectively, less than or equal to 4, 3, 2, and 1. We also show that the coefficient R4,n(x) can be written as
Boukhemis Ammar, Zerouki Ebtissem
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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-
Koepf, Wolfram, Schmersau, Dieter
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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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Classical Orthogonal Polynomials Revisited
Results in Mathematics, 2023 AbstractThis manuscript contains a small portion of the algebraic theory of orthogonal polynomials developed by Maroni and their applicability to the study and characterization of the classical families, namely Hermite, Laguerre, Jacobi, and Bessel polynomials.
K. Castillo, J. Petronilho
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On Certain Properties and Applications of the Perturbed Meixner–Pollaczek Weight
Mathematics, 2021 This paper deals with monic orthogonal polynomials orthogonal with a perturbation of classical Meixner–Pollaczek measure. These polynomials, called Perturbed Meixner–Pollaczek polynomials, are described by their weight function emanating from an ...
Abey S. Kelil +2 more
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The Stenger conjectures and the A-stability of collocation Runge-Kutta methods
Journal of Inequalities and Applications, 2023 Stenger conjectures are claims about the location of the eigenvalues of matrices whose elements are certain integrals involving basic Lagrange interpolating polynomials supported on the zeros of orthogonal polynomials. In this paper, we show the validity
Rachid Ait-Haddou, Hoda Alselami
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Ural Mathematical Journal, 2022 In this paper, we introduce the concept of the \(\mathbb{B}_{\alpha}\)-classical orthogonal polynomials, where \(\mathbb{B}_{\alpha}\) is the raising operator \(\mathbb{B}_{\alpha}:=x^2 \cdot {d}/{dx}+\big(2(\alpha-1)x+1\big)\mathbb{I}\), with nonzero ...
Baghdadi Aloui, Jihad Souissi
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Krylov complexity and orthogonal polynomials
Nuclear Physics B, 2022 Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method.
Wolfgang Mück, Yi Yang
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RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS
Проблемы анализа, 2020 We consider recurrence relations for the polynomials orthonormal with respect to the Sobolev-type inner product and generated by classical orthogonal polynomials, namely: Jacobi polynomials, Legendre polynomials, Chebyshev polynomials of the first and ...
M. S. Sultanakhmedov
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Fourier coefficients for Laguerre–Sobolev type orthogonal polynomials [PDF]
Arab Journal of Mathematical Sciences, 2023 Purpose – In this paper, the authors take the first step in the study of constructive methods by using Sobolev polynomials. Design/methodology/approach – To do that, the authors use the connection formulas between Sobolev polynomials and classical ...
Alejandro Molano
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