Results 11 to 20 of about 6,848 (171)
DARBOUX TRANSFORMS AND ORTHOGONAL POLYNOMIALS [PDF]
Bulletin of the Korean Mathematical Society, 2002 In [\textit{F. A. Grünbaum} and \textit{L. Haine}, Symmetries and Integrability of Differential Equations, Estérel, 1994, CRM Proc. Lect. Notes 9, 143-154 (1996; Zbl 0865.33008)] the Darboux transform was used to obtain so-called Bochner-Krall orthogonal polynomials which satisfy a higher order (\(>2\)) spectral type differential equation. This Darboux
Gang-Joon Yoon
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Homogeneous darboux polynomials and generalising integrable ODE systems
Journal of Computational Dynamics, 2021 We show that any system of ODEs can be modified whilst preserving its homogeneous Darboux polynomials. We employ the result to generalise a hierarchy of integrable Lotka-Volterra systems.
van der Kamp, Peter H. +2 more
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A Christoffel–Darboux formula for multiple orthogonal polynomials
Journal of Approximation Theory, 2004 11 pages, no ...
Daems, E., Kuijlaars, A.B.J.
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Asymptotics of Meixner polynomials and Christoffel–Darboux kernels [PDF]
Transactions of the Moscow Mathematical Society, 2013 Summary: We obtain the asymptotics of the classical Meixner polynomials \(M_n(x)\) (orthogonal with respect to a discrete measure supported at the nonnegative integer points) and the corresponding reproducing kernels (Christoffel-Darboux kernels) \(K_n(x,y)\) as \(n\) and the variable \(x\) tend to infinity under various relationships between their ...
Aptekarev, A. I., Tulyakov, D. N.
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Journal of Physics A: Mathematical and Theoretical, 2010 Simple derivation is presented of the four families of infinitely many shape invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi polynomials.
Agarwal R P +19 more
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On the Darboux transformations and sequences of p-orthogonal polynomials [PDF]
Applied Mathematics and Computation, 2020 For a fixed $p \in \mathbb{N}$, sequences of polynomials $\{P_n\}$, $n \in \mathbb{N}$, defined by a $(p+2)$-term recurrence relation are related to several topics in Approximation Theory. A $(p+2)$-banded matrix $J$ determines the coefficients of the recurrence relation of any of such sequences of polynomials.
Barrios Rolanía, Maria Dolores +2 more
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On the Christoffel–Darboux formula for generalized matrix orthogonal polynomials
Journal of Mathematical Analysis and Applications, 2014 We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal ...
Carlos Álvarez-Fernández +1 more
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Darboux polynomials and first integrals of natural polynomial Hamiltonian systems [PDF]
Physics Letters A, 2004 We show that for a natural polynomial Hamiltonian system the existence of a single Darboux polynomial (a partial polynomial first integral) is equivalent to the existence of an additional first integral functionally independent with the Hamiltonian function.
Maciejewski, Andrzej J. +1 more
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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials [PDF]
, 2013 We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic ...
Gomez-Ullate, David +2 more
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On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D [PDF]
Theoretical and Applied Mechanics, 2017 The first integrals of the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the Oregonator model are derived using the method of Darboux polynomials.
Esen Oğul +2 more
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