Results 201 to 210 of about 14,680 (235)
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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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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. ∗
Ronveaux, André +3 more
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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, 2018In this paper, the authors introduce Hahn-Appell polynomial sequences by the following property \[ D_{q,\omega} P_n(x)=[n] P_{n-1}(x), \qquad n\geq 1, \] where \(D_{q,\omega}\) is the Hahn \((q,\omega)\) -difference operator and \([n]=\frac{1-q^n}{1-q}\).
Serhan Varma +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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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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On a generalized homogeneous Hahn polynomial
Science China Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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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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