Results 31 to 40 of about 619 (209)
New Bounds for Hahn and Krawtchouk Polynomials [PDF]
SIAM Journal on Mathematical Analysis, 1995 For the Hahn and Krawtchouk polynomials orthogonal on the set $\{0, \ldots,N\}$ new identities for the sum of squares are derived which generalize the trigonometric identity for the Chebyshev polynomials of the first and second kind. These results are applied in order to obtain conditions (on the degree of the polynomials) such that the polynomials are
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Hahn polynomials on polyhedra and quantum integrability
Advances in Mathematics, 2020 Orthogonal polynomials with respect to the hypergeometric distribution on lattices in polyhedral domains in ${\mathbb R}^d$, which include hexagons in ${\mathbb R}^2$ and truncated tetrahedrons in ${\mathbb R}^3$, are defined and studied. The polynomials are given explicitly in terms of the classical one-dimensional Hahn polynomials.
Plamen Iliev, Yuan Xu
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Doubling (Dual) Hahn Polynomials: Classification and Applications [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2016 We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The idea and interest comes from an example appearing in a finite oscillator model [Jafarov E.I., Stoilova N.I., Van der Jeugt J., J. Phys. A: Math. Theor.
Oste, Roy, Van der Jeugt, Joris
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Some results on biorthogonal polynomials
International Journal of Mathematics and Mathematical Sciences, 1994 Some biorthogonal polynomials of Hahn and Pastro are derived using a polynomial modification of the Lebesgue measure dθ combined with analytic continuation. A result is given for changing the measures of biorthogonal polynomials on the unit circle by the
Richard W. Ruedemann
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The orthogonal Shmaliy polynomials are Hahn polynomials
, 2021 Morales-Mendoza et al. present in 2013 a new class of discrete orthogonal polynomials. They use these polynomials to design an unbiased FIR filter. In their paper they make the statement that a representation of the polynomials via hypergeometric functions is unknown. However Shakibaei Asli et al.
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Orthogonal polynomials and Stieltjes functions: the Laguerre-Hahn case [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1996 In this paper we consider orthogonal polynomials of the so-called Laguerre-Hahn class. This means that the Stieltjes function associated with the corresponding moment sequence satisfies a Riccati differential equation with polynomial coefficients.
E. PRIANES, F. MARCELLÁN
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Bivariate Hahn moments for image reconstruction
International Journal of Applied Mathematics and Computer Science, 2014 This paper presents a new set of bivariate discrete orthogonal moments which are based on bivariate Hahn polynomials with non-separable basis. The polynomials are scaled to ensure numerical stability.
Wu Haiyong, Yan Senlin
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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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Some New Generating Functions for q-Hahn Polynomials
Journal of Applied Mathematics, 2014 We obtain some new generating functions for q-Hahn polynomials and give their proofs based on the homogeneous q-difference operator.
Yun Zhou, Qiu-Ming Luo
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On Perfectness of Systems of Weights Satisfying Pearson’s Equation with Nonstandard Parameters
Axioms, 2023 Measures generating classical orthogonal polynomials are determined by Pearson’s equation, whose parameters usually provide the positivity of the measures.
Alexander Aptekarev +2 more
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