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Zeros of Sobolev Orthogonal Polynomials of Gegenbauer Type

Journal of Approximation Theory, 2002
This paper is devoted to the study of the location of the zeros of the Sobolev polynomials \(S_n\), where \(\{S_n\}_n\) are the monic orthogonal polynomial sequences with respect to the Sobolev inner product. First the author recalls some well known properties of Gegenbauer polynomials, which are used in the following.
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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, 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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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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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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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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Moment representation of Bernoulli polynomial, Euler polynomial and Gegenbauer polynomials

Statistics & Probability Letters, 2007
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Polynomials Associated With Gegenbauer Polynomials

The Fibonacci Quarterly, 1981
A. F. Horadam, S. Pethe
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A New Comprehensive Subclass of Analytic Bi-Univalent Functions Related to Gegenbauer Polynomials

Symmetry, 2023
Tariq Al-Hawary, Ala Amourah, Abdullah Alsoboh   +2 more
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