Results 211 to 220 of about 446,531 (268)

A Subclass of Bi-univalent Functions Defined by aSymmetric q-Derivative Operator and Gegenbauer Polynomials

European Journal of Pure and Applied Mathematics
This paper introduces a novel subclass of bi-univalent analytic functions by utilizing a symmetric q-derivative operator in conjunction with Gegenbauer polynomials.
Mohamed Illafe, M. Mohd, Feras Yousef, Shamani Supramaniam   +3 more
semanticscholar   +1 more source

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.
openaire   +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
openaire   +1 more source

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
openaire   +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.
De Micheli Enrico, Viano Giovanni Alberto   +1 more
openaire   +2 more sources

Bidimensional Gegenbauer Polynomials for Variable‐Order Time‐Fractional Integro‐Partial Differential Equation With a Weakly Singular Kernel

Mathematical methods in the applied sciences
In this paper, a pseudo‐operational collocation method based on Gegenbauer polynomials is presented to solve a category of variable‐order time‐fractional integro‐partial differential equations with singular kernels.
S. Yaghoubi, H. Aminikhah, K. Sadri
semanticscholar   +1 more source

Mixed-type hypergeometric Bernoulli-Gegenbauer polynomials: some properties

Communications in Applied and Industrial Mathematics
We consider the novel family of the mixed-type hypergeometric Bernoulli-Gegenbauer polynomials. This family represents a fascinating fusion between two distinct categories of special functions: hypergeometric Bernoulli polynomials and Gegenbauer ...
Dionisio Peralta, Yamilet Quintana
semanticscholar   +1 more source

Uniform Asymptotic Expansions for Gegenbauer Polynomials and Related Functions via Differential Equations Having a Simple Pole

Constructive approximation, 2022
Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order n that are uniformly valid for unbounded complex values of the argument z , including the real interval $$0 \le z \le 1$$ 0 ≤ z ≤ 1 in which the zeros in the ...
T. M. Dunster
semanticscholar   +1 more source

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
openaire   +1 more source

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.
openaire   +1 more source