Results 221 to 230 of about 441,925 (264)

Gegenbauer Polynomials Revisited

The Fibonacci Quarterly, 1985
Der Gegenstand dieser Arbeit sind spezielle Polynome, die sich in der Tafel der Gegenbauerschen Polynome entlang der abnehmenden Diagonalen bilden. Dabei werden einige Eigenschaften dieser Polynome diskutiert wie z.B. expliziter Ausdruck, erzeugende Funktion, rekurrenter Ausdruck, Differentialgleichung u.s.w.
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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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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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Bidimensional Gegenbauer Polynomials for Variable‐Order Time‐Fractional Integro‐Partial Differential Equation With a Weakly Singular Kernel

Mathematical methods in the applied sciences
In this paper, a pseudo‐operational collocation method based on Gegenbauer polynomials is presented to solve a category of variable‐order time‐fractional integro‐partial differential equations with singular kernels.
S. Yaghoubi, H. Aminikhah, K. Sadri
semanticscholar   +1 more source

Uniform Asymptotic Expansions for Gegenbauer Polynomials and Related Functions via Differential Equations Having a Simple Pole

Constructive approximation, 2022
Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order n that are uniformly valid for unbounded complex values of the argument z , including the real interval $$0 \le z \le 1$$ 0 ≤ z ≤ 1 in which the zeros in the ...
T. M. Dunster
semanticscholar   +1 more source

Uniform inequalities for Gegenbauer polynomials

Acta Mathematica Hungarica, 1996
The usual asymptotic representations of the Gegenbauer (ultraspherical) polynomials do not yield bounds on their absolute values which hold equally on the interval \(-1\leq x\leq 1\). But in the Legendre case (index \(\lambda= {1\over 2}\)) and more generally in the case of \(0\leq \lambda\leq 1\) such estimates exist.
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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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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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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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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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