Results 181 to 190 of about 634 (218)
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SIAM Journal on Mathematical Analysis, 1970
The Hahn Polynomials are discrete analogues of the Jacobi polynomials. Here we try to ascertain the depth of the analogy, by examining the relation between these two sets. We also obtain bounds on the integral of the Hahn polynomial which corresponds to the Legendre polynomial.
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The Hahn Polynomials are discrete analogues of the Jacobi polynomials. Here we try to ascertain the depth of the analogy, by examining the relation between these two sets. We also obtain bounds on the integral of the Hahn polynomial which corresponds to the Legendre polynomial.
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Journal of Mathematical Physics, 1993
Continuous Hahn polynomials Sn(x) appear in a formulation of quantum mechanics on a discrete time lattice, where they form a natural basis for the state vectors. In this paper we derive some of their generating functions, the expression of the raising and lowering operators and give a lower bound for the largest root of the equation Sn(x)=0.
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Continuous Hahn polynomials Sn(x) appear in a formulation of quantum mechanics on a discrete time lattice, where they form a natural basis for the state vectors. In this paper we derive some of their generating functions, the expression of the raising and lowering operators and give a lower bound for the largest root of the equation Sn(x)=0.
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Journal of Physics A: Mathematical and General, 1985
A slightly more general orthogonality relation for the Hahn polynomials of a continuous variable than the recent one given by \textit{N. M. Atakishiev} and \textit{S. K. Suslov} [ibid. 18, 1583-1596 (1985; reviewed above)] is given here.
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A slightly more general orthogonality relation for the Hahn polynomials of a continuous variable than the recent one given by \textit{N. M. Atakishiev} and \textit{S. K. Suslov} [ibid. 18, 1583-1596 (1985; reviewed above)] is given here.
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The Zeros of the Hahn Polynomials
SIAM Review, 1967x = 0, 1, * , n 1. From this it follows when a, d> -1 that, if y is an integer > mn, the zeros of Pm(` 7)(x) are real and simple and lie in the open interval (0, y 1). In the present paper this conclusion is extended to all real -y > mn and also to 7y < -(im + ae + d) with (d + -y, -a 1) as the interval containing the zeros in the latter case.
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Continuous Hahn polynomials and the Heisenberg algebra
Journal of Mathematical Physics, 1987Continuous Hahn polynomials have surfaced in a number of somewhat obscure physical applications. For example, they have emerged in the description of two-photon processes in hydrogen, hard-hexagon statistical mechanical models, and Clebsch–Gordan expansions for unitary representations of the Lorentz group SO(3,1).
Carl M. Bender +2 more
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Multivariable biorthogonal Hahn polynomials
Journal of Mathematical Physics, 1989A multivariable biorthogonal generalization of the discrete Hahn polynomials, a p+1 complex parameter family, where p is the number of variables, is presented. It is shown that the polynomials are orthogonal with respect to subspaces of lower degree and biorthogonal within a given subspace.
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Multivariable continuous Hahn polynomials
Journal of Mathematical Physics, 1988A multivariable generalization of the continuous Hahn polynomials is presented; it is a (4p+4)-parameter family, where p is the number of variables. It is shown that they are orthogonal with respect to subspaces of equal degree and biorthogonal within a given subspace. In the simplest case the multivariable weight function takes the form sech[π(x1+x2+⋅⋅
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Stable Computation of Hahn Polynomials for Higher Polynomial Order
2020 International Conference on Intelligent Systems and Computer Vision (ISCV), 2020In this paper, we propose a new algorithm for computing Hahn polynomial coefficients (HPCs) for higher polynomial order, which greatly reduces the spread of numerical defects associated with Hahn polynomials (HPs) using conventional methods. The proposed method is used to reconstruct large 2D images.
Mhamed Sayyouri +3 more
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A Positive Kernel for Hahn–Eberlein Polynomials
SIAM Journal on Mathematical Analysis, 1978Explicit forms of the coefficients $E(x,y,z)$ in the expansion $Q_n (x)Q_n (y) = \sum_{z = 0}^N {E(x,y,z)} Q_n (z)$, where $Q_n (x) = Q_n (x;\alpha ,\beta ,N)$ is the Hahn polynomial in the integer-valued variable x, $0 \leqq x \leqq N$, are given. It is shown that if $\alpha \leqq \beta N - 1$.
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Associated dual Hahn polynomials
1988A generating function, the spectral measure and two explicit forms are obtained for each of the two families of associated continuous dual Hahn polynomials.
Mourad E. H. Ismail +2 more
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