Results 71 to 80 of about 122,453 (243)
Spectral analysis for the exceptional Xm-Jacobi equation
Electronic Journal of Differential Equations, 2015 We provide the mathematical foundation for the $X_m$-Jacobi spectral theory. Namely, we present a self-adjoint operator associated to the differential expression with the exceptional $X_m$-Jacobi orthogonal polynomials as eigenfunctions.
Constanze Liaw +2 more
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Orthogonal polynomials of discrete variable and boundedness of Dirichlet kernel
, 2005 For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined.
Obermaier, Josef, Szwarc, Ryszard
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An upper bound on Jacobi polynomials
Journal of Approximation Theory, 2007 Let ${\bf P}_k^{( , )} (x)$ be an orthonormal Jacobi polynomial of degree $k.$ We will establish the following inequality \begin{equation*} \max_{x \in [ _{-1}, _1]}\sqrt{(x- _{-1})( _1-x)} (1-x)^ (1+x)^ ({\bf P}_{k}^{( , )} (x))^2 < \frac{3 \sqrt{5}}{5}, \end{equation*} where $ _{-1}
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On Saigo Fractional $q$-Calculus of a General Class of $q$-Polynomials [PDF]
Sahand Communications in Mathematical AnalysisIn this paper, we derive Saigo fractional $q$-integrals of the general class of $q$-polynomials and demonstrate their application by investigating $q$-Konhouser biorthogonal polynomial, $q$-Jacobi polynomials and basic analogue of the Kamp$\acute{e}$ de
Biniyam Shimelis, Dayalal Suthar
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Shifted Jacobi polynomials and Delannoy numbers [PDF]
arXiv, 2009 We express a weighted generalization of the Delannoy numbers in terms of shifted Jacobi polynomials. A specialization of our formulas extends a relation between the central Delannoy numbers and Legendre polynomials, observed over 50 years ago, to all Delannoy numbers and certain Jacobi polynomials.
arxiv
Mathematics, 2018 This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim +3 more
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Generating functions for the Jacobi polynomial [PDF]
Proceedings of the American Mathematical Society, 1976 Two theorems are proved with the aid of operator and series iteration methods. Special cases appear to give new and known generating functions for the Jacobi polynomial.
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Riemann–Liouville Operator in Weighted Lp Spaces via the Jacobi Series Expansion
Axioms, 2019 In this paper, we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann−Liouville fractional integral and derivative operators on a compact of the real axis.
Maksim V. Kukushkin
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The Stenger conjectures and the A-stability of collocation Runge-Kutta methods
Journal of Inequalities and Applications, 2023 Stenger conjectures are claims about the location of the eigenvalues of matrices whose elements are certain integrals involving basic Lagrange interpolating polynomials supported on the zeros of orthogonal polynomials. In this paper, we show the validity
Rachid Ait-Haddou, Hoda Alselami
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, 2005 The analytic solutions of the one-dimensional Schroedinger equation for the trigonometric Rosen-Morse potential reported in the literature rely upon the Jacobi polynomials with complex indices and complex arguments.
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