Results 11 to 20 of about 1,201 (100)

A generating function and formulae defining the first-associated Meixner–Pollaczek polynomials [PDF]

Integral Transforms and Special Functions, 2018
While considering nonlinear coherent states with specific anti-holomorphic coefficients $\bar{z}^n/\sqrt{x_n!}$, we identify as first associated Meixner-Pollaczek polynomials the orthogonal polynomials arising from shift operators which are defined by the sequence $x_n=(n+1)^2$ .
Ahbli, Khalid, Mouayn, Zouhair
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Multiple Meixner–Pollaczek polynomials and the six-vertex model

Journal of Approximation Theory, 2011
We study multiple orthogonal polynomials of Meixner-Pollaczek type with respect to a symmetric system of two orthogonality measures. Our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to a constrained vector equilibrium problem.
Bender, Martin, Delvaux, Steven, Kuijlaars, Arno B.J.   +2 more
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Generalized coherent states for oscillators connected with Meixner and Meixner—Pollaczek polynomials [PDF]

Journal of Mathematical Sciences, 2006
The investigation of the generalized coherent states for oscillator-like systems connected with given family of orthogonal polynomials is continued. In this work we consider oscillators connected with Meixner and Meixner-Pollaczek polynomials and define generalized coherent states for these oscillators.
Borzov, V. V., Damaskinskiĭ, E. V.
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Operator orderings and Meixner-Pollaczek polynomials [PDF]

Journal of Mathematical Physics, 2013
The aim of this paper is to give identities which are generalizations of the formulas given by Koornwinder [J. Math. Phys. 30, 767–769 (1989)]10.1063/1.528394 and Hamdi-Zeng [J. Math. Phys. 51, 043506 (2010)]10.1063/1.3372526. Our proofs are much simpler than and different from the previous investigations.
Genki Shibukawa
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Uniform asymptotics for Meixner–Pollaczek polynomials with varying parameters

Comptes Rendus. Mathématique, 2011
In this Note, we study the uniform asymptotics of the Meixner–Pollaczek polynomials Pn(λn)(z;ϕ) with varying parameter λn=(n+12)A as n→∞, where A>0 is a constant. Uniform asymptotic expansions in terms of parabolic cylinder functions and elementary functions are obtained for z in two overlapping regions which together cover the whole complex plane.
Wang, Jun, Qiu, Weiyuan, Wong, Roderick
openaire   +3 more sources

Bounds for extreme zeros of Meixner–Pollaczek polynomials

Journal of Approximation Theory
In this paper we consider connection formulae for orthogonal polynomials in the context of Christoffel transformations for the case where a weight function, not necessarily even, is multiplied by an even function $c_{2k}(x),k\in N_0$, to determine new lower bounds for the largest zero and upper bounds for the smallest zero of a Meixner-Pollaczek ...
A.S. Jooste, K. Jordaan
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The symmetric Meixner–Pollaczek polynomials with real parameter

Journal of Mathematical Analysis and Applications, 2005
The symmetric Meixner-Pollaczek polynomials \(p_n^\lambda(x)\) can be determinated by the generating function \[ {{\exp (x\arctan t)}\over {(1+t^2)^\lambda}}=\sum_{n=0}^\infty p_n^\lambda(x) t^n,\quad \lambda\in\mathcal R. \] It is well known that these polynomials are orthogonal with the weight \[ \omega_\lambda(x)= { 1\over {2\pi}} \biggl| \Gamma ...
Tsehaye K. Araaya
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On the Meixner–Pollaczek polynomials and the Sturm–Liouville problems

Journal of Mathematical Analysis and Applications
This work provides a detailed study of Meixner-Pollaczek polynomials and employs the central difference operator to study the Sturm-Liouville problem. It presents two linearly independent solutions to the recursion relation, along with the associated difference equations. Additionally, the establishment of second-kind functions is discussed.
Mourad E.H. Ismail, Nasser Saad
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The Meixner–Pollaczek polynomials and a system of orthogonal polynomials in a strip

Journal of Computational and Applied Mathematics, 2004
Two systems of polynomials \(\{\tau_n\}\) and \(\{\sigma_n\}\) which satisfy the recursion relations \[ \tau_{n+1}(z)=z\tau_n(z)-n^2\tau_{n-1}(z), \quad n\geq0, \qquad \tau_{-1}=0, \;\tau_0=1 \] and \[ \sigma_{n+1}(z)=z\sigma_n(z)-n(n-1)\sigma_{n-1}(z), \quad n\geq0, \qquad \sigma_{-1}=0, \;\sigma_0=1, \] respectively, are under consideration in the ...
Tsehaye K. Araaya
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Orthogonality of the Meixner-Pollaczek polynomials beyond Favard's theorem

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Moreno, Samuel G., García-Caballero, Esther M.   +1 more
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