Results 1 to 10 of about 246 (165)
A new operational matrix of fractional derivative based on the generalized Gegenbauer–Humbert polynomials to solve fractional differential equations [PDF]
Alexandria Engineering Journal, 2021 In this paper, a new type of wavelet method to solve fractional differential equations (linear or nonlinear) is proposed. The proposed method is based on the generalized Gegenbauer–Humbert polynomial.
Jumana H.S. Alkhalissi +4 more
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Some identities involving generalized Gegenbauer polynomials [PDF]
Advances in Difference Equations, 2017 In this paper, we investigate some interesting identities on the Bernoulli, Euler, Hermite and generalized Gegenbauer polynomials arising from the orthogonality of generalized Gegenbauer polynomials in the generalized inner product 〈 p 1 ( x ) , p 2 ( x )
Zhaoxiang Zhang
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Generalized and mixed type Gegenbauer polynomials [PDF]
Journal of Mathematical Analysis and Applications, 2012 Using the integral representation method and the monomiality principle (see e.g.[\textit{G. Dattoli}, Advanced special functions and applications. Proceedings of the workshop, Melfi, Italy, May 9-12, 1999. Rome: Aracne Editrice. Proc. Melfi Sch. Adv. Top. Math. Phys.
Subuhi Khan, Ahmed Ali Al-Gonah
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An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials [PDF]
Advances in Applied Mathematics, 2002 In this interesting paper the author studies generalized Gegenbauer polynomials that are orthogonal with respect to the weight function \(|x|^{2\mu}\) \((1-x^2)^{\lambda- {1\over 2}}\). First, an important integral formula is established for these polynomials that serves as a transformation between \(h\)-harmonics of different parameters and contains ...
Xu, Yuan
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Application of Gegenbauer Polynomials with Two Variables to Bi-univalency of Generalized Discrete Probability Distribution Via Zero-Truncated Poisson Distribution Series [PDF]
Sahand Communications in Mathematical AnalysisThe present study is unique in exploring bi-univalent functions, which has recently garnered attention from many researchers in Geometric Function Theory (GFT).
Tunji Ibrahim Awolere +2 more
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The affine group and generalized Gegenbauer polynomials [PDF]
Computers and Mathematics With Applications, 2001 Let \((\xi_1,\xi_2)\) denote a basis of the Lie algebra \(\mathbb{L}\) of the affine group with commutator relation \([\xi_1,\xi_2] =\xi_2\). Representing \(\mathbb{L}\) by the action on polynomials leads to the investigation of operators of the following type: Put \(\xi_1= x\cdot D+\alpha\) (for some constant \(\alpha)\), i.e. \(\xi_1x^n= (n+\alpha) x^
Feinsilver, Ph., Franz, U.
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On Generating Relations Involving Generalized Gegenbauer Polynomials [PDF]
Georgian Mathematical Journal, 2006 Abstract In this paper, generating relations involving generalized Gegenbauer polynomials are obtained by constructing a three-dimensional Lie algebra isomorphic to special linear algebra sl(2). Further, a number of new interesting relations involving various generalized polynomials are obtained as applications of these generating ...
Subuhi Khan
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Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials
Mathematics, 2023 In this paper, we consider a 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 ...
Dionisio Peralta +2 more
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A Generalization of Gegenbauer Polynomials and Bi-Univalent Functions
Axioms, 2023 Three subclasses of analytic and bi-univalent functions are introduced through the use of q−Gegenbauer polynomials, which are a generalization of Gegenbauer polynomials. For functions falling within these subclasses, coefficient bounds a2 and a3 as well as Fekete–Szegö inequalities are derived. Specializing the parameters used in our main results leads
Gharib Gharib +2 more
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On a generalization of the generating function for Gegenbauer polynomials [PDF]
Integral Transforms and Special Functions, 2013 A generalization of the generating function for Gegenbauer polynomials is introduced whose coefficients are given in terms of associated Legendre functions of the second kind. We discuss how our expansion represents a generalization of several previously derived formulae such as Heine's formula and Heine's reciprocal square-root identity.
Howard Cohl
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