Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals [PDF]
International Journal of Mathematics and Mathematical Sciences, 1980 Using the technique of canonical expansion in probability theory, a bilinear summation formula is derived for the special case of the Meixner-Pollaczek polynomials {λn(k)(x)} which are defined by the generating function ∑n=0∞λn(k)(x)zn/n!=(1+z)12(x−k)/(1−
P. A. Lee
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On Certain Properties and Applications of the Perturbed Meixner–Pollaczek Weight
Mathematics, 2021 This paper deals with monic orthogonal polynomials orthogonal with a perturbation of classical Meixner–Pollaczek measure. These polynomials, called Perturbed Meixner–Pollaczek polynomials, are described by their weight function emanating from an ...
Abey S. Kelil +2 more
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Deformed su(1,1) Algebra as a Model for Quantum Oscillators [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2012 The Lie algebra su(1,1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su}(1,1) can be extended to representations of this deformed algebra su(1,1)_gamma.
Elchin I. Jafarov +2 more
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A new class of coherent states with Meixner-Pollaczek polynomials for the Gol'dman-Krivchenkov Hamiltonian [PDF]
Journal of Physics A: Mathematical and Theoretical, 2010 A class of generalized coherent states with a new type of the identity resolution are constructed by replacing the labeling parameter zn/n! of the canonical coherent states by Meixner-Pollaczek polynomials with specific parameters.
Ali S T +12 more
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Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions [PDF]
, 2018 Burchnall's method to invert the Feldheim-Watson linearization formula for the Hermite polynomials is extended to all polynomial families in the Askey-scheme and its $q$-analogue.
Ismail, Mourad E. H. +2 more
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Generalized Meixner-Pollaczek polynomials
Advances in Difference Equations, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kanas, Stanislawa, Tatarczak, Anna
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Meixner–Pollaczek polynomials and the Heisenberg algebra [PDF]
Journal of Mathematical Physics, 1989 An alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. Phys. 28, 509 (1987)].
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New connection formulae for some q-orthogonal polynomials in q-Askey scheme [PDF]
, 2007 New nonlinear connection formulae of the q-orthogonal polynomials, such continuous q-Laguerre, continuous big q-Hermite, q-Meixner-Pollaczek and q-Gegenbauer polynomials, in terms of their respective classical analogues are obtained using a special ...
A Yanallah +7 more
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Linearly-invariant families and generalized Meixner–Pollaczek polynomials
Annales UMCS, Mathematica, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Naraniecka, Iwona +2 more
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Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials [PDF]
MATHEMATICA SCANDINAVICA, 2017 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: orthogonality, generating and determinantal formulae, difference equations.
Faraut, Jacques, Wakayama, Masato
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