Results 221 to 230 of about 446,531 (268)

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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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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Subclasses of bi-univalent functions subordinate to gegenbauer polynomials

Afrika Matematika, 2023
A. Amourah, Z. Salleh, B. Frasin, Muhammad Ghaffar Khan, B. Ahmad   +4 more
semanticscholar   +1 more source

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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Bivariate Densities with Diagonal Expansions in Gegenbauer Polynomials

Journal of the Franklin Institute, 1977
Abstract Closed-form expressions and diagonal series expansions in Gegenbauer polynomials are derived for two bivariate density functions.
Derin, H., Wise, G. L., Thomas, J. B.
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An Efficient Numerical Scheme to Approach the Time Fractional Black–Scholes Model Using Orthogonal Gegenbauer Polynomials

Computational Economics, 2023
Y. E. Aghdam, H. Mesgarani, A. Amin, J. F. Gómez‐Aguilar   +3 more
semanticscholar   +1 more source

On a subclass of bi-univalent functions affiliated with bell and Gegenbauer polynomials

Boletim da Sociedade Paranaense de Matemática
This research paper explores the development of a novel class of analytic bi-univalent functions, leveraging the Bell polynomials along with the Gegenbauer polynomials as a fundamental component for establishing the new subclass.
Mohamed Illafe, Abdulmtalb Hussen, M. Mohd, Feras Yousef   +3 more
semanticscholar   +1 more source

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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