Results 141 to 150 of about 320 (175)

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).
Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner   +2 more
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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.
Vasudevan Lakshminarayanan, L. Srinivasa Varadharajan   +1 more
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Information entropy of Gegenbauer polynomials

Journal of Physics A: Mathematical and General, 2000
Summary: The information entropy of Gegenbauer polynomials is relevant since this is related to the angular part of the information entropies of certain quantum mechanical systems such as the harmonic oscillator and the hydrogen atom in \(D\) dimensions.
Buyarov, V. S., López-Artés, P., Martínez-Finkelshtein, A., Van Assche, W.   +3 more
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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 ...
Francisco Marcellán, Teresa E. Pérez, Miguel A. Piñar   +2 more
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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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Information entropy of Gegenbauer polynomials and Gaussian quadrature

Journal of Physics A: Mathematical and General, 2003
\textit{V. S. Buyarov}, \textit{P. López-Artés}, \textit{A. Martínez-Finkelshtein} and \textit{W. van Assche} [J. Phys. A, Math. Gen. 33, No. 37, 6549--6560 (2000; Zbl 1008.81015)] used two auxiliary polynomials to evaluate the information entropy of the Gegenbauer polynomials \(C^{(\lambda)}_n(x)\) in the case when one of the polynomials used was \(P ...
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New Proof of the Addition Theorem for Gegenbauer Polynomials

SIAM Journal on Mathematical Analysis, 1971
The quantity $(\lambda - z)^\rho $ is expanded in Jacobi polynomials $P_n^{(\alpha ,\beta )} (z)$, where $\alpha $, $\beta $, and $\rho $ are unrelated. The known case $\alpha = \beta = - \rho - 1$ is then used in a short proof of the addition theorem for Gegenbauer polynomials.
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Polynomials Associated With Gegenbauer Polynomials

The Fibonacci Quarterly, 1981
A. F. Horadam, S. Pethe
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An expansion for gegenbauer polynomials

USSR Computational Mathematics and Mathematical Physics, 1965
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