Results 11 to 20 of about 886 (183)
Generalized Jacobi Weights, Christoffel Functions, and Jacobi Polynomials [PDF]
SIAM Journal on Mathematical Analysis, 1994 Let \(\omega(x)= (1- x)^ \alpha(1+ x)^ \beta\), \(\alpha>-1\), \(\beta>- 1\), \(x\in [-1,1]\), and let \(\{p_ n(\omega,x)\}\) be the set of Jacobi polynomials which are orthogonal with respect to \(\omega(x)\) over \([- 1,1]\). With a view to determining the constant involved in the known inequality (\textit{L. Gatteschi} [SIAM J. Math. Anal.
Nevai, Paul +2 more
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Exceptional Jacobi polynomials [PDF]
Journal of Approximation Theory, 2019 40 pages, 1 ...
Niels Bonneux
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q-Calculus as operational algebra; pp. 73–97 [PDF]
Proceedings of the Estonian Academy of Sciences, 2009 This second paper on operational calculus is a continuation of Ernst, T. q-Analogues of some operational formulas. Algebras Groups Geom., 2006, 23(4), 354â374. We find multiple q-analogues of formulas in Carlitz, L.
Thomas Ernst
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Jacobi's Generating Function for Jacobi Polynomials [PDF]
Proceedings of the American Mathematical Society, 1978 An idea of Hermite is used to give a simple proof of Jacobi’s generating function for Jacobi polynomials.
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A note on pseudo Jacobi polynomials
Ain Shams Engineering Journal, 2013 The present paper is a study of pseudo-Jacobi polynomials which have been defined on the pattern of Shively’s pseudo-Laguerre polynomials. The paper contains generating functions, Rodrigues formula, recurrence relations and expansion of pseudo-Jacobi ...
Mumtaz Ahmad Khan +2 more
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RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS
Проблемы анализа, 2020 We consider recurrence relations for the polynomials orthonormal with respect to the Sobolev-type inner product and generated by classical orthogonal polynomials, namely: Jacobi polynomials, Legendre polynomials, Chebyshev polynomials of the first and ...
M. S. Sultanakhmedov
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Parameter Derivatives of the Jacobi Polynomials with Three Variables on the Simplex
MATEC Web of Conferences, 2016 In this paper, an attempt has been made to derive parameter derivatives of Jacobi polynomials with three variables on the simplex. They are obtained via parameter derivatives of the classical Jacobi polynomials Pn(α,β)(x) with respect to their parameters.
Aktaş Rabia
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Iterated Integrals of Jacobi Polynomials [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2019 Let P(α,β)n be the n-th monic Jacobi polynomial with α,β>−1. Given m numbers ω1,…,ωm∈C∖[−1,1], let Ωm=(ω1,…,ωm) and P(α,β)n,m,Ωm be the m-th iterated integral of (n+m)!n!P(α,β)n normalized by the conditions dkP(α,β)n,m,Ωmdzk(ωm−k)=0, for k=0,1,…,m−1. The main purpose of the paper is to study the algebraic and asymptotic properties of the sequence of ...
Hector Pijeira-Cabrera +1 more
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Some generalized Jacobi polynomials
Computers & Mathematics with Applications, 2003 Following the work of the first author [Int. J. Math. Math. Sci. 24, No. 10, 673--689 (2000; Zbl 0967.33006)] in this paper the authors obtain the explicit expressions for the coefficients in the three term pure recurrence relation for generalized Jacobi polynomials defined by a positive weight function which involves a \(p\)th power of \((1-x)\).
Atia, M.J., Alaya, J., Ronveaux, A.
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Exceptional Jacobi polynomials which are deformations of Jacobi polynomials
Journal of Mathematical Analysis and Applications, 2023 Exceptional polynomials are complete orthogonal polynomial systems with respect to a positive measure in the real line which in addition are eigenfunctions of a second order differential operator. The most apparent difference between classical orthogonal polynomials and their exceptional counterparts is that the exceptional families have gaps in their ...
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