Results 181 to 190 of about 619 (209)

Continuous Hahn polynomials

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 Atakishiyev and Suslov, (1985), is given here.
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The Zeros of the Hahn Polynomials

SIAM Review, 1967
x = 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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Multivariable biorthogonal Hahn polynomials

Journal of Mathematical Physics, 1989
A 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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Continuous Hahn polynomials and the Heisenberg algebra

Journal of Mathematical Physics, 1987
Continuous 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, Lawrence R. Mead, Stephen S. Pinsky   +2 more
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Associated dual Hahn polynomials

1988
A 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, Jean Letessier, Galliano Valent   +2 more
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Multivariable continuous Hahn polynomials

Journal of Mathematical Physics, 1988
A 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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Hahn-Appell polynomials and their d-orthogonality

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018
Recently, parametric $$(q,\omega )$$ -exponential functions were defined in [4]. In the present paper, we obtain non-parametric Hahn exponential functions by using the characteristic properties of the usual ...
Serhan Varma, Banu Yılmaz Yaşar, Mehmet Ali Özarslan   +2 more
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Bernstein bases and hahn—eberlein orthogonal polynomials

Integral Transforms and Special Functions, 1998
Expansions of continuous and discrete Bernsein bases on shifted Jacobi and Hahn polynomials, respectively, are explicitly obtained in terms of Hahn-Eberlein orthogonal polynomials. The basic tool is an algorighm, recently developed by the authors, which allows one to solve the connection problem between two families of polynomials recurrently. ∗
A. Zarzo, Iván Area, André Ronveaux, Eduardo Godoy   +3 more
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A Positive Kernel for Hahn–Eberlein Polynomials

SIAM Journal on Mathematical Analysis, 1978
Explicit 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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Spectral accuracy for the Hahn polynomials

2016
We consider in this paper the Hahn polynomials and their application in numerical methods. The Hahn polynomials are classical discrete orthogonal polynomials. We analyse the behaviour of these polynomials in the context of spectral approximation of partial differential equations.
Goertz, Ren��, ��ffner, Philipp
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