Results 211 to 220 of about 561,686 (251)

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 \textit{N. M. Atakishiev} and \textit{S. K. Suslov} [ibid. 18, 1583-1596 (1985; reviewed above)] is given here.
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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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Carlitz's q‐Operators for the Generalized Homogeneous Hahn Polynomials

Mathematical methods in the applied sciences
In this paper, motivated by Carlitz's q$$ q $$ ‐operators and Liu's generalized homogeneous Hahn polynomials, we show how to construct Carlitz's q$$ q $$ ‐operators of the generalized homogeneous Hahn polynomials.
Jian Cao, H. M., Yue Zhang
semanticscholar   +1 more source

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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A $$q$$q-extension of a partial differential equation and the Hahn polynomials

, 2015
Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $$q$$q-partial differential equations, then, it can be expanded in terms of the product of the ...
Zhi-Guo Liu
semanticscholar   +1 more source

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. ∗
Ronveaux, André, Zarzo, A., Area, I., Godoy, E.   +3 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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Periodic reduction of the factorization chain and the Hahn polynomials

Journal of Physics A: Mathematical and General, 1994
Summary: The \(N = 4\) periodic closure of the factorization chain is considered. It is shown that the nonlinear operator algebra corresponding to this closure can be transformed into the quadratic Hahn algebra. As a result, the three-term recurrence coefficients for the Hahn polynomials provide a special realization of the \(N = 4\) periodic ...
Spiridonov, Vyacheslav, Vinet, Luc, Zhedanov, Alexei   +2 more
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An efficient approach based on Legendre-Gauss–Lobatto quadrature and discrete shifted Hahn polynomials for solving Caputo–Fabrizio fractional Volterra partial integro-differential equations

Journal of Computational and Applied Mathematics, 2021
H. Dehestani, Y. Ordokhani
semanticscholar   +1 more source