Results 11 to 20 of about 139,435 (183)
anar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2023 A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same polynomials are also type I orthogonal polynomials on a contour, provided the exponents in the weight are ...
Berezin, Sergey +2 more
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Equivalences of the Multi-Indexed Orthogonal Polynomials [PDF]
, 2013 Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion.
Odake, Satoru
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Some Orthogonal Polynomials Arising from Coherent States [PDF]
, 2011 We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature.
Akhiezer N I +19 more
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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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Planar orthogonal polynomials as Type II multiple orthogonal polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2019 We show that the planar orthogonal polynomials with $l$ logarithmic singularities in the potential are the multiple orthogonal polynomials (Hermite-Pad polynomials) of Type II with $l$ measures. We also find the ratio between the determinant of the moment matrix corresponding to the multiple orthogonal polynomials and the determinant of the moment ...
Seung-Yeop Lee, Meng Yang
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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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Integral of Legendre polynomials and its properties [PDF]
Mathematics and Computational SciencesThis paper is concerned with deriving a new system of orthogonal polynomials whose inflection points coincide with their interior roots, primitives of Legendre polynomials.
Abdelhamid Rehouma
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Проблемы анализа, 2020 In this paper, we give the generating functions of binary product between 2-orthogonal Chebyshev polynomials and kFibonacci, k-Pell, k-Jacobsthal numbers and the other orthogonal Chebyshev polynomials.
H. Merzouk, B. Aloui, A. Boussayoud
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Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space
International Journal of Mathematics and Mathematical Sciences, 2004 A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions.
Fred Brackx +2 more
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On some hypergeometric Sobolev orthogonal polynomials with several continuous parameters
Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2023 In this paper we study the following hypergeometric polynomials: $$ \mathcal{P}_n(x) = \mathcal{P}_n(x;\alpha,\beta,\delta_1, \dots,\delta_\rho,\kappa_1,\dots,\kappa_\rho) = $$ $$ = {}_{\rho+2} F_{\rho+1} (-n,n+\alpha+\beta+1,\delta_1+1, \dots,\delta_ ...
Sergey Zagorodnyuk
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