Results 141 to 150 of about 110,049 (182)
Generalized and mixed type Gegenbauer polynomials [PDF]
Journal of Mathematical Analysis and Applications, 2012 In this paper, a new generalized form of the Gegenbauer polynomials is introduced by using the integral representation method. Further, the Hermite–Gegenbauer and the Laguerre–Gegenbauer polynomials are introduced by using the operational identities ...
Subuhi Khan +2 more
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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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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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Computing with Expansions in Gegenbauer Polynomials
SIAM Journal of Scientific Computing, 2009We 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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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
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Derivatives of Generalized Gegenbauer Polynomials
Theoretical and Mathematical Physics, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
García Fuertes, W., Perelomov, A. M.
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New generating functions for Gegenbauer polynomials [PDF]
Journal of Computational and Applied Mathematics, 1996 A family of new generating functions for the Gegenbauer polynomials is presented. This work is based upon the elementary manipulation of series and is motivated by the recent appearance of these polynomials in certain aspects of applied ...
Exton, Harold
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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
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Gegenbauer Polynomials Revisited
The Fibonacci Quarterly, 1985Der 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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On the Behavior of Gegenbauer Polynomials in the Complex Plane
Results in Mathematics, 2012A 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, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Eelbode, Tim Janssens
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