Results 1 to 10 of about 429 (105)
Gegenbauer polynomials and the Fueter theorem [PDF]
Complex Variables and Elliptic Equations, 2013 The Fueter theorem states that regular (resp. monogenic) functions in quaternionic (resp. Clifford) analysis can be constructed from holomorphic functions in the complex plane, hereby using a combination of a formal substitution and the action of an appropriate power of the Laplace operator.
David Eelbode +2 more
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Generalized Gegenbauer orthogonal polynomials
Journal of Computational and Applied Mathematics, 2001 AbstractIn this paper we explore a specific semi-classical orthogonal sequence, namely the generalized Gegenbauer orthogonal polynomials (GG) which appear in many applications such as the weighted Lp mean convergence of Hermite–Fejér interpolation or the chain of harmonic oscillators in the absence of externally applied forces.
S. Belmehdi
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Information entropy of Gegenbauer polynomials of integer parameter [PDF]
Journal of Physics A: Mathematical and Theoretical, 2007 19 pages, 1 Postscript ...
Julio I. de Vicente +2 more
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Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials
Journal of Computational and Applied Mathematics, 1997 Publicado
Andrei Martı́nez-Finkelshtein +2 more
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Exceptional Gegenbauer polynomials via isospectral deformation
Studies in Applied Mathematics, 2021 AbstractIn this paper, we show how to construct exceptional orthogonal polynomials (XOP) using isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux transformations, where repeated factorizations at the same eigenvalue are allowed. These factorizations allow us to construct Sturm–Liouville problems
María Ángeles García‐Ferrero +3 more
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Generalized and mixed type Gegenbauer polynomials
Journal of Mathematical Analysis and Applications, 2012 AbstractIn this paper, a new generalized form of the Gegenbauer polynomials is introduced by using the integral representation method. Further, the Hermite–Gegenbauer and the Laguerre–Gegenbauer polynomials are introduced by using the operational identities associated with the generalized Hermite and Laguerre polynomials of two variables.
Subuhi Khan +2 more
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On the asymptotic expansion of the entropy of Gegenbauer polynomials
Journal of Computational and Applied Mathematics, 2002 AbstractIn this paper, the third term in the asymptotic expansion of the entropy for orthonormal Gegenbauer polynomials with fixed integer parameter is obtained as the degree of the polynomials tends to infinity, improving the results of Buyarov et al. (J. Phys. A 33 (2000) 6549).
J.F. Sánchez-Lara
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On an umbral treatment of Gegenbauer, Legendre and Jacobi polynomials [PDF]
International Mathematical Forum, 2017 Special polynomials, ascribed to the family of Gegenbauer, Legen- dre, and Jacobi and of their associated forms, can be expressed in an operational way, which allows a high degree of flexibility for the for- mulation of the relevant theory. We develop a point of view based on an umbral type formalism, exploited in the past, to study some aspects of the
G. Dattoli +3 more
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Orthogonal polynomials for the oscillatory-Gegenbauer weight [PDF]
Publications de l'Institut Mathematique, 2008 This is a continuation of our previous investigations on polynomials orthogonal with respect to the linear functional L : P?C, where L = ?1 -1 p(x) d?(x), d?(x) = (1-x?)?-1/2 exp(i?x) dx, and P is a linear space of all algebraic polynomials. Here, we prove an extension of our previous existence theorem for rational ? ? (-1/2,0], give some hypothesis on
Gradimir V. Milovanović +2 more
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On the derivatives of generalized Gegenbauer polynomials
, 2002 Preprint.
W. Garcı́a Fuertes, A. M. Perelomov
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