Results 201 to 210 of about 6,433 (235)

Higher Spin Generalisation of the Gegenbauer Polynomials

Complex Analysis and Operator Theory, 2016
In this paper we generalise the harmonic Gegenbauer polynomials to the higher spin setting. To do so we will consider the space of simplicial harmonics and look for polynomials that are invariant with respect to a particular subalgebra of the orthogonal Lie algebra.
David Eelbode, Tim Janssens
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Appendix: Gegenbauer Polynomials

2016
This chapter collects some properties of the Gegenbauer polynomials that we use throughout this work, in particular, in the proof of the explicit formulae for differential symmetry breaking operators (Theorems 1.5, 1.6, 1.7, and 1.8) and the factorization identities for special parameters (Theorems 13.1, 13.2, and 13.3).
Michael Pevzner, Toshiyuki Kobayashi, Toshihisa Kubo   +2 more
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The expansion in Gegenbauer polynomials: A simple method for the fast computation of the Gegenbauer coefficients

Journal of Computational Physics, 2013
We present a simple and fast algorithm for the computation of the Gegenbauer transform, which is known to be very useful in the development of spectral methods for the numerical solution of ordinary and partial differential equations of physical interest.
De Micheli Enrico, Viano Giovanni Alberto   +1 more
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On the use of Gegenbauer polynomials in the synthesis of arrays [PDF]

IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC/CNC/URSI North American Radio Sci. Meeting (Cat. No.03CH37450), 2004
The paper reconsiders the application of the Gegenbauer polynomials to the design of directive linear/planar arrays. The shape of the resulting radiation pattern fits typical specifications better than classical choices, as the Gegenbauer profile allows the specifications to be satisfied on the sidelobe levels for two distinct angles.
Morini A, Rozzi T, Venanzoni, Giuseppe, Chiarandini S.   +3 more
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On the Behavior of Gegenbauer Polynomials in the Complex Plane [PDF]

Results in Mathematics, 2012
It is well-known that the squared modulus of every function f from the Laguerre–Polya class $${\mathcal{L}-\mathcal{P}}$$ of entire functions obeys a MacLaurin series representation $$|f(x ...
Alexander Alexandrov, Geno Nikolov
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The relativistic Hermite polynomial is a Gegenbauer polynomial

Journal of Mathematical Physics, 1994
It is shown that the polynomials introduced recently by Aldaya, Bisquert, and Navarro-Salas [Phys. Lett. A 156, 381 (1991)] in connection with a relativistic generalization of the quantum harmonic oscillator can be expressed in terms of Gegenbauer polynomials. This fact is useful in the investigation of the properties of the corresponding wave function.
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Gegenbauer, Jacobi, and Orthogonal Polynomials

2016
In earlier chapters we dealt with special sets of orthogonal polynomials, namely, Chebyshev and Hermite polynomials. In Chs. 9 and 10 we will study other orthogonal polynomials, namely, Laguerre and Legendre. All of these polynomial functions share many properties.
L. Srinivasa Varadharajan, Vasudevan Lakshminarayanan   +1 more
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ON GEGENBAUER POLYNOMIALS

Universal Journal of Mathematics and Mathematical Sciences, 2021
U. E. Edeke, N. E. Udo
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Computing with Expansions in Gegenbauer Polynomials

SIAM Journal on Scientific Computing, 2009
We develop fast algorithms for computations involving finite expansions in Gegenbauer polynomials. A method is described to convert any finite expansion between different families of Gegenbauer polynomials. For a degree-$n$ expansion the computational cost is $\mathcal{O}(n(\log(1/\varepsilon)+|\alpha-\beta|))$, where $\varepsilon$ is the prescribed ...
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Gegenbauer-Sobolev Orthogonal Polynomials

1994
In this paper, orthogonal polynomials in the Sobolev space W 1,2([-1,1], p (α),λ p (α)), where \({\rho ^{(\alpha )}} = {(1 - {x^2})^{\alpha - \frac{1}{2}}},\alpha >- \frac{1}{2}\) and λ ≥ 0, are studied. For these non-standard orthogonal polynomials algebraic and differential properties are obtained, as well as the relation with the classical ...
Teresa E. Pérez, Miguel A. Piñar, Francisco Marcellán   +2 more
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