Results 161 to 170 of about 263,554 (202)

Computing with Expansions in Gegenbauer Polynomials

SIAM Journal of 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 ...
exaly   +2 more sources

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.
Enrico De Micheli, Giovanni Alberto Viano   +1 more
exaly   +3 more sources

ON GEGENBAUER POLYNOMIALS

Universal Journal of Mathematics and Mathematical Sciences, 2021
Summary: In this paper, it is shown that the terms of Gegenbauer polynomial satisfy the Jacobi identity.
Edeke, U. E., Udo, N. E.
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A Rodrigues-type formula for Gegenbauer matrix polynomials [PDF]

Applied Mathematics Letters, 2013
This paper centers on the derivation of a Rodrigues-type formula for the Gegenbauer matrix polynomial. A connection between Gegenbauer and Jacobi matrix polynomials is givenThis research has been supported by the Universitat Politecnica de Valencia under
Defez Candel, Emilio
exaly   +2 more sources

Derivatives of Generalized Gegenbauer Polynomials

Theoretical and Mathematical Physics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
García Fuertes, W., Perelomov, A. M.
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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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Results on the associated Jacobi and Gegenbauer polynomials [PDF]

Journal of Computational and Applied Mathematics, 1993
Recurrence relations for the coefficients of the Jacobi polynomial form of the associated Jacobi polynomials P(α,β)n(x; c) are given. For certain values of α, β, explicit formulae for these coefficients are obtained.
Stanisław Lewanowicz
exaly   +2 more sources

On the Behavior of Gegenbauer Polynomials in the Complex Plane

Results in Mathematics, 2012
A real entire function \(f\) is said to be in the the Laguerre-Pólya class, denoted by \(\mathcal L\)-\(\mathcal P\), if \(f\) is the uniform limit, on compact subsets of \(\mathbb C\), of polynomials all of whose zeros are real. If \(f\in \mathcal L\text{-}\mathcal P\), then it is known that \[ |f(x+iy)|^2=\sum_{k=0}^{\infty} L_k(f; x)y^{2k},\quad x ...
Nikolov, Geno, Alexandrov, Alexander
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Higher Spin Generalisation of the Gegenbauer Polynomials

Complex Analysis and Operator Theory, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Eelbode, Tim Janssens
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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).
Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner   +2 more
openaire   +1 more source