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Characterization of classical type orthogonal polynomials [PDF]
Proceedings of the American Mathematical Society, 1994 We characterize the classical type orthogonal polynomials { P n ( x ) } 0 ∞ \{ {P_n}(x)\} _0^\infty satisfying a fourth-order differential equation of type \[ ∑ i
KWON, KH Kwon, Kil Hyun +3 more
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SECOND STRUCTURE RELATION FOR THE DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
Проблемы анализа, 2023 In this paper, we characterize the Dunkl-classical orthogonal polynomials by a second structure relation.
Y. Habbachi
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A conjecture on Exceptional Orthogonal Polynomials [PDF]
, 2012 Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials.
A. González-López +42 more
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Communications, 2010 In applications of mathematics involving either the Laplace or the Helmholtz equation in spherical coordinates the associated Legendre equation occurs. Its solutions are called associated Legendre functions. They have some relations to classical Legendre
Vladimir Guldan, Mariana Marcokova
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Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure [PDF]
, 2015 This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure for x in [0,?), ?
Alfredo Deaño +28 more
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On 2-orthogonal polynomials of Laguerre type
International Journal of Mathematics and Mathematical Sciences, 1999 Let {Pn}n≥0 be a sequence of 2-orthogonal monic polynomials relative to linear functionals ω0 and ω1 (see Definition 1.1). Now, let {Qn}n≥0 be the sequence of polynomials defined by Qn:=(n+1)−1P′n+1,n≥0.
Khalfa Douak
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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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q-Hermite Polynomials and Classical Orthogonal Polynomials [PDF]
Canadian Journal of Mathematics, 1996 AbstractWe use generating functions to express orthogonality relations in the form of q-beta. integrals. The integrand of such a q-beta. integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials ...
Christian Berg, Mourad E. H. Ismail
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International Journal of Mathematics and Mathematical Sciences, 2000 We give explicitly the recurrence coefficients of a nonsymmetric semi-classical sequence of polynomials of class s=1. This sequence generalizes the Jacobi polynomial sequence, that is, we give a new orthogonal sequence {Pˆn(α,α+1)(x,μ)}, where μ is an ...
Mohamed Jalel Atia
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A NOTE FOR THE DUNKL-CLASSICAL POLYNOMIALS
Проблемы анализа, 2022 In this paper, we give a new characterization for the Dunkl-classical orthogonal polynomials. The previous characterization has been illustrated by some examples.
Y. Habbachi, B. Bouras
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