Results 11 to 20 of about 909 (183)
Two-dimensional limit series in ultraspherical Jacobi polynomials and their approximative properties [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021 Let $C[-1,1]$ be the space of functions continuous on the segment $[-1,1]$, $C[-1,1]^2$ be the space of functions continuous on the square $[-1,1]^2$. We denote by $P_n^\alpha(x)$ the ultraspherical Jacobi polynomials.
Guseinov, Ibraghim G. +1 more
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On the Direct Limit from Pseudo Jacobi Polynomials to Hermite Polynomials
Mathematics, 2021 In this short communication, we present a new limit relation that reduces pseudo-Jacobi polynomials directly to Hermite polynomials. The proof of this limit relation is based upon 2F1-type hypergeometric transformation formulas, which are applicable to ...
Elchin I. Jafarov +2 more
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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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Jacobi Polynomials on the Bernstein Ellipse [PDF]
Journal of Scientific Computing, 2017 In this paper, we are concerned with Jacobi polynomials $P_n^{(α,β)}(x)$ on the Bernstein ellipse with motivation mainly coming from recent studies of convergence rate of spectral interpolation. An explicit representation of $P_n^{(α,β)}(x)$ is derived in the variable of parametrization. This formula further allows us to show that the maximum value of $
Haiyong Wang, Lun Zhang
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On the Approximation of the Jacobi Polynomials
Rocky Mountain Journal of Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Elias, Uri, Gingold, Harry
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Integral of Legendre polynomials and its properties [PDF]
Mathematics and Computational SciencesThis paper is concerned with deriving a new system of orthogonal polynomials whose inflection points coincide with their interior roots, primitives of Legendre polynomials.
Abdelhamid Rehouma
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Bispectral Jacobi type polynomials [PDF]
Advances in Applied Mathematics, 2022 23 pages.
Antonio J. Durán +1 more
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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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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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