Results 121 to 130 of about 5,592 (152)

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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The Application of Gegenbauer Polynomials to the Michell Integral

Journal of Ship Research, 1972
Gegenbauer polynomials have been used to define the centerplane distribution of Havelock sources defining the ship in the Michell thin-ship theory. Orthogonality properties have been used to reduce the Michell integral to a double finite sum of coefficients defined in terms of the singularity distribution, the Froude number, and the length-draft ratio.
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On spectral identities involving Gegenbauer polynomials

The Journal of Analysis, 2019
The Gegenbauer coefficients $$c_{j}^{\ell }(\nu )$$ ( $$1\le j\le \ell ;\, \nu >-1/2$$
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A new family of degenerate poly-Bernoulli polynomials of the second kind with its certain related properties

AIMS Mathematics, 2021
Waseem Ahmad Khan, Abdulghani Muhyi, Rifaqat Ali   +2 more
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