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Bernstein bases and hahn—eberlein orthogonal polynomials
Integral Transforms and Special Functions, 1998Expansions 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 +3 more
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Hahn Polynomials, Discrete Harmonics, andt-Designs
SIAM Journal on Applied Mathematics, 1978Let \(L_q(v)\) be the lattice of subsets of a given \(v\)-set or the lattice of the subspaces of a given \(v\)-dimensional vector space over \(\mathrm{GF}(q)\), in case \(q=1\) or \(q= \text{prime}\) power, respectively. Denote by \(X\) the vertex set of the lattice, by \(\le\) the ordering relation, by \(\wedge\) and \(\vee\) the meet and joint ...
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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, 2018Recently, 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 +2 more
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Hahn class orthogonal polynomials
1998The authors find several sets of equivalent conditions for orthogonal polynomials to satisfy the operator equation \[ p_2(x) \delta^2 y\bigl ((x-w)/q\bigr)+ p_1(x)\delta y\bigl((x-w)/q \bigr)= \lambda_ny(x) \] where \(\delta\) is Hahn's operator, \(p_2(x)\) and \(p_1(x)\) are polynomials of degrees at most two and one, and \(\lambda_n\) is an ...
Kil H. Kwon +3 more
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A Generalization of Gasper's Kernel for Hahn Polynomials: Application to Pollaczek Polynomials
Canadian Journal of Mathematics, 1978In this paper we consider a generalization of the discrete Poisson kernel for the Hahn polynomials obtained recently by Gasper [6]. The Hahn polynomials of degree n are defined by and are ...
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Product Formulas for q-Hahn Polynomials
SIAM Journal on Mathematical Analysis, 1980Product formulas for general q-Hahn polynomials are derived from counting arguments involving subspaces of a finite vector space.
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An Addition Theorem for Hahn Polynomials: The Spherical Functions
SIAM Journal on Mathematical Analysis, 1978An addition formula for the Hahn polynomials $Q_k (x;\alpha ,\beta ,N)$ is derived for the parameter values $\beta = - N - 1$, $\alpha \ne - 1, - 2, \cdots , - N$, $N = 1,2,3, \cdots $. The method is to realize $Q_k $ as a spherical function for the values $\alpha = - N - 1, - N - 2, \cdots $ and to use harmonic analysis on the finite homogeneous space
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Entanglement and control of single nuclear spins in isotopically engineered silicon carbide
Nature Materials, 2020Alexandre Bourassa +2 more
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