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]
, 2023 Kareem T. Elgindy, Hareth M. Refat
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On the local time of random walks associated with Gegenbauer polynomials [PDF]
arXiv, 2010 The local time of random walks associated with Gegenbauer polynomials $P_n^{(\alpha)}(x),\ x\in [-1,1]$ is studied in the recurrent case: $\alpha\in\ [-\frac{1}{2},0]$. When $\alpha$ is nonzero, the limit distribution is given in terms of a Mittag-Leffler distribution.
arxiv
Quantum algebra approach to q Gegenbauer polynomials
Journal of Computational and Applied Mathematics, 1995 AbstractQuantum algebras provide a natural algebraic setting for q special functions. The matrix elements of certain algebra generators in irreducible representations are in fact expressible in terms of q hypergeometric series. Taking the quantum algebra U((1,1)) as example, we shall show that its metaplectic representation provides a group-theoretic ...
Roberto Floreanini, Luc Vinet
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An interesting application of Gegebauer Polynomials [PDF]
arXiv, 2010 In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.
arxiv
Results on the associated Jacobi and Gegenbauer polynomials
Journal of Computational and Applied Mathematics, 1993 AbstractRecurrence 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. In particular, the classical Watson formula for the first associated Gegenbauer polynomials is generalized.
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Adomian decomposition method by Gegenbauer and Jacobi polynomials
International Journal of Computer Mathematics, 2011 In this paper, orthogonal polynomials on [–1,1] interval are used to modify the Adomian decomposition method (ADM). Gegenbauer and Jacobi polynomials are employed to improve the ADM and compared with the method of using Chebyshev and Legendre polynomials.
Cenesiz, Yucel, Kurnaz, Aydin
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Multivariate positive definite functions on spheres [PDF]
AMS Series: Conteporary Mathematics, vol. 625 (2014), 177-190, 2007 In 1942 I. J. Schoenberg proved that a function is positive definite in the unit sphere if and only if this function is a positive linear combination of the Gegenbauer polynomials. In this paper we extend Schoenberg's theorem for multivariate Gegenbauer polynomials.
arxiv
Rényi Entropies of Multidimensional Oscillator and Hydrogenic Systems with Applications to Highly Excited Rydberg States. [PDF]
Entropy (Basel), 2022 Dehesa JS.
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Functionals of Gegenbauer polynomials and D-dimensional hydrogenic momentum expectation values [PDF]
, 2000 Walter Van Assche +3 more
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Jaynes-Gibbs Entropic Convex Duals and Orthogonal Polynomials. [PDF]
Entropy (Basel), 2022 Le Blanc R.
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