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Expansion of the Riemann Ξ Function in Meixner–Pollaczek Polynomials

Canadian mathematical bulletin, 2008
A. Kuznetsov
semanticscholar   +1 more source

The Meixner-Pollaczek and Meixner Polynomials in Discrete Quantum Mechanics

In this paper the Meixner-Pollaczek and Meixner polynomials are used to solve the Schrödinger difference equation in discrete quantum mechanics for particular potentials. Shift operators and difference operators defining discrete quantum mechanical model are introduced, together with orthogonal polynomials that allow to exactly solve these models for ...
Barrie, Emily, Hedenstedt, Joel
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Barnes type integral and the Meixner-Pollaczek polynomials

Barnes type integral and the Meixner-Pollaczek polynomials
identifier:oai:t2r2.star.titech.ac.jp ...
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Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials

Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials
Harmonic analysis on Hermitian symmetric spaces of tube type is a natural framework for introducing multivariate Meixner-Pollaczek polynomials. Their main properties are established in this setting: generating and determinantal formulae, difference equations.
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Asymptotic relations between the Hahn-type polynomials and Meixner-Pollaczek, Jacobi, Meixner and Krawtchouk polynomials

, 2008
Chelo Ferreira, J. López, E. P. Sinusía   +2 more
semanticscholar   +1 more source

Multivariate Meixner-Pollaczek polynomials and an application (Perspectives of Representation Theory and Noncommutative Harmonic Analysis)

Multivariate Meixner-Pollaczek polynomials and an application (Perspectives of Representation Theory and Noncommutative Harmonic Analysis)
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Certain results on generating functions related to the associated Meixner-Pollaczek polynomials

Integral Transforms and Special Functions, 2021
In the present paper we first derive a new form of a generating function for the c-associated Meixner-Pollaczek polynomials.
Min-Jie Luo, Ravinder Krishna Raina, Shu-Han Zhao   +2 more
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On the Asymptotics of the Meixner—Pollaczek Polynomials and Their Zeros

Constructive Approximation, 2001
An infinite asymptotic expansion is derived for the Meixner-Pollaczek polynomials \(M_n(n\alpha; \delta,n)\) as \(n\to\infty\), which holds uniformly for \(-M\leq\alpha\leq M\), where \(M\) can be any positive number. This expansion involves the parabolic cylinder function and its derivative.
Li, X., Wong, R.
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Global Asymptotics for Meixner‐Pollaczek Polynomials with a Varying Parameter

Studies in Applied Mathematics, 2013
In this paper, we study the uniform asymptotics of the Meixner‐Pollaczek polynomials with varying parameter as , where A > 0 is a constant. Two asymptotic expansions are obtained, which hold uniformly for z in two overlapping regions which together cover the whole complex plane.
Wang, Jun, Qiu, Weiyuan, Wong, R.
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Some Continued Fractions of Ramanujan and Meixner-Pollaczek Polynomials

Canadian Mathematical Bulletin, 1989
AbstractWe examine the convergence and analytic properties of a continued fraction of Ramanujan and its connection to the orthogonal polynomials of Meixner-Pollaczek.
D. Masson
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