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Czasopisma help

  1. 4 Open Mathematics

Autorzy help

  1. 2 Weber H.

  2. 1 Dominici D.

  3. 1 Zhao W.

Lata help

  1. 1 2010

  2. 3 2007

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1
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Asymptotic analysis of the Askey-scheme I: from Krawtchouk to Charlier

100%
Dominici D.
Open Mathematics
|
2007
|
tom 5
|
nr 2
280-304
EN
We analyze the Charlier polynomials C n(χ) and their zeros asymptotically as n → ∞. We obtain asymptotic approximations, using the limit relation between the Krawtchouk and Charlier polynomials, involving some special functions. We give numerical examples showing the accuracy of our formulas.
2
Content available remote

A deformation of commutative polynomial algebras in even numbers of variables

100%
Zhao W.
Open Mathematics
|
2010
|
tom 8
|
nr 1
73-97
EN
We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right and left total symbols of differential operators of polynomial algebras. Furthermore, a more conceptual re-formulation for the image conjecture [18] is also given in terms of the deformed algebras. Consequently, the well-known Jacobian conjecture [8] is reduced to an open problem on this deformation of polynomial algebras.
3
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Connections between Romanovski and other polynomials

84%
Weber H.
Open Mathematics
|
2007
|
tom 5
|
nr 3
581-595
EN
A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.
4
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Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

84%
Weber H.
Open Mathematics
|
2007
|
tom 5
|
nr 2
415-427
EN
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.
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