Subclasses of Yamakawa-Type Bi-Starlike Functions Associated with Gegenbauer Polynomials [PDF]
Axioms, 2022 In this paper, we introduce and investigate new subclasses (Yamakawa-type bi-starlike functions and another class of Lashin, both mentioned in the reference list) of bi-univalent functions defined in the open unit disk, which are associated with the ...
G. Murugusundaramoorthy +1 more
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A direct integral pseudospectral method for solving a class of infinite-horizon optimal control problems using Gegenbauer polynomials and certain parametric maps [PDF]
AIMS Mathematics, 2022 We present a novel direct integral pseudospectral (PS) method (a direct IPS method) for solving a class of continuous-time infinite-horizon optimal control problems (IHOCs).
Kareem T. Elgindy, Hareth M. Refat
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On the asymptotic expansion of the entropy of Gegenbauer polynomials
Journal of Computational and Applied Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J.F. Sánchez-Lara
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Generalized and mixed type Gegenbauer polynomials
Journal of Mathematical Analysis and Applications, 2012 AbstractIn 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 associated with the generalized Hermite and Laguerre polynomials of two variables.
Subuhi Khan +2 more
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Exceptional Gegenbauer polynomials via isospectral deformation
Studies in Applied Mathematics, 2021 AbstractIn this paper, we show how to construct exceptional orthogonal polynomials (XOP) using isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux transformations, where repeated factorizations at the same eigenvalue are allowed. These factorizations allow us to construct Sturm–Liouville problems
María Ángeles García‐Ferrero +3 more
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Ultraspherical/Gegenbauer polynomials to unify 2D/3D Ambisonic directivity designs
arXiv.orgThis report on axisymmetric ultraspherical/Gegenbauer polynomials and their use in Ambisonic directivity design in 2D and 3D presents an alternative mathematical formalism to what can be read in, e.g., my and Matthias Frank's book on Ambisonics or J\'er\^
Franz Zotter
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Weighted L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document}-norms of Gegenbauer polynomials [PDF]
Aequationes mathematicae, 2022 We study integrals of the form \begin{equation*} \int_{-1}^1(C_n^{( )}(x))^2(1-x)^ (1+x)^ \, dx, \end{equation*} where $C_n^{( )}$ denotes the Gegenbauer-polynomial of index $ >0$ and $ , >-1$. We give exact formulas for the integrals and their generating functions, and obtain asymptotic formulas as $n\to\infty$.
J. Brauchart, P. Grabner
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European Journal of Pure and Applied MathematicsIn this paper, we introduce and investigate a class of bi-univalent functions, denoted by $\mathcal{F}(n, \alpha, \beta)$, that depends on the Ruscheweyh operator.
Waleed Al-Rawashdeh
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On an umbral treatment of Gegenbauer, Legendre and Jacobi polynomials [PDF]
International Mathematical Forum, 2017 Special polynomials, ascribed to the family of Gegenbauer, Legen- dre, and Jacobi and of their associated forms, can be expressed in an operational way, which allows a high degree of flexibility for the for- mulation of the relevant theory. We develop a point of view based on an umbral type formalism, exploited in the past, to study some aspects of the
G. Dattoli +3 more
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Direct integral pseudospectral and integral spectral methods for solving a class of infinite horizon optimal output feedback control problems using rational and exponential Gegenbauer polynomials [PDF]
Mathematics and Computers in Simulation, 2023 Kareem T. Elgindy, Hareth M. Refat
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