Results 1 to 10 of about 50 (50)
Classical Orthogonal Polynomials Revisited
Results in Mathematics, 2023 AbstractThis manuscript contains a small portion of the algebraic theory of orthogonal polynomials developed by Maroni and their applicability to the study and characterization of the classical families, namely Hermite, Laguerre, Jacobi, and Bessel polynomials.
K. Castillo, J. Petronilho
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Asymptotic Computation of Classical Orthogonal Polynomials [PDF]
, 2021 The classical orthogonal polynomials (Hermite, Laguerre and Jacobi) are involved in a vast number of applications in physics and engineering. When large degrees $n$ are needed, the use of recursion to compute the polynomials is not a good strategy for computation and a more efficient approach, such as the use of asymptotic expansions,is recommended. In
Amparo Gil, Javier Segura, Nico M. Temme
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Some classical multiple orthogonal polynomials [PDF]
Journal of Computational and Applied Mathematics, 2001 Recently there has been a renewed interest in an extension of the notion of orthogonal polynomials known as multiple orthogonal polynomials. This notion comes from simultaneous rational approximation (Hermite-Pade approximation) of a system of several functions.
Els Coussement, Walter Van Assche
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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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A ‘missing’ family of classical orthogonal polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2011 We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can be obtained from the little $q$-Jacobi polynomials in the limit $q=-1$.
Alexei Zhedanov, Luc Vinet
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d-Orthogonal Analogs of Classical Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 Classical orthogonal polynomial systems of Jacobi, Hermite and Laguerre have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they are the only systems on the real line with this property.
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Extensions of discrete classical orthogonal polynomials beyond the orthogonality
Journal of Computational and Applied Mathematics, 2009 It is well known that the family of Hahn polynomials $\{h_n^{ , }(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $ $-Sobolev orthogonality.
Costas-Santos, Roberto S. +1 more
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On an system of “classical” polynomials of simultaneous orthogonality
Journal of Computational and Applied Mathematics, 1996 AbstractWe introduce a system of “classical” polynomials of simultaneous orthogonality, study the differential equation of third order, recurrence relation and precise the ratio asymptotic and zeros distribution of polynomials.
André Ronveaux, V. Kaliaguine
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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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On a new characterization of the classical orthogonal polynomials
Journal of Approximation Theory, 1992 AbstractIn this paper we give a new characterization of the classical orthogonal polynomials (Jacobi, Laguerre, and Hermite polynomials) by a special property of the sequences in their recurrence formula. The results also allow an easy derivation of the asymptotic distribution of the zeros of the classical orthogonal polynomials.
Holger Dette, W. J. Studden
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