Results 41 to 50 of about 607 (135)

An upper bound on Jacobi polynomials

Journal of Approximation Theory, 2007
Let ${\bf P}_k^{(α, β)} (x)$ be an orthonormal Jacobi polynomial of degree $k.$ We will establish the following inequality \begin{equation*} \max_{x \in [δ_{-1},δ_1]}\sqrt{(x- δ_{-1})(δ_1-x)} (1-x)^α(1+x)^β ({\bf P}_{k}^{(α, β)} (x))^2 < \frac{3 \sqrt{5}}{5}, \end{equation*} where $δ_{-1}
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Classification of Exceptional Jacobi Polynomials

Studies in Applied Mathematics
ABSTRACT We provide a full classification scheme for exceptional Jacobi operators and polynomials. The classification contains six degeneracy classes according to whether or assume integer values. Exceptional Jacobi operators are in one‐to‐one correspondence with spectral diagrams, a combinatorial object that describes the quasi ...
Garcia-Ferrero, Maria Angeles, Gomez-Ullate, David, Milson, Robert   +2 more
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Multiple Wilson and Jacobi–Piñeiro polynomials

Journal of Approximation Theory, 2005
22 pages, 2 ...
Bernhard Beckermann, J. Coussement, Walter Van Assche   +2 more
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Biorthogonal polynomials suggested by the Jacobi polynomials [PDF]

Pacific Journal of Mathematics, 1982
Madhekar, H. C., Thakare, N. K.
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On the maximum value of Jacobi polynomials

Journal of Approximation Theory, 2005
A remarkable inequality with utterly explicit constants established by Erdélyi, Magnus and Nevai states that for \(\alpha\geq \beta> -{1\over 2}\) the orthonormal Jacobi polynomials \(P^{(\alpha,\beta)}_k\) satisfy \[ M(P^{(\alpha,\beta)}_k, \sqrt{1- x^2})= \max_{|x|\leq 1} \{(1- x)^{\alpha+{1\over 2}}(1+ x)^{\beta+{1\over 2}}(P^{(\alpha,\beta)}_k(x ...
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The kernel polynomial method based on Jacobi polynomials

Applied Mathematics and Computation
The kernel polynomial method based on Jacobi polynomials $P_n^{α,β}(x)$ is proposed. The optimal-resolution positivity-preserving kernels and the corresponding damping factors are obtained. The results provide a generalization of the Jackson damping factors for arbitrary Jacobi polynomials.
I.O. Raikov, Y.M. Beltukov
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Representation of [Formula: see text]-Bernstein polynomials in terms of [Formula: see text]-Jacobi polynomials. [PDF]

J Inequal Appl, 2017
Soleyman F, Area I, Masjed-Jamei M, Nieto JJ.   +3 more
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From coin tossing to the jacobi polynomials

Journal of Combinatorial Theory, Series A, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A class of matrix-valued polynomials generalizing Jacobi polynomials

Journal of Approximation Theory, 2009
A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a two-step recurrence relation, integral inter-relations, and quasi-orthogonality relations.
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New formulae for the high-order derivatives of some Jacobi polynomials: an application to some high-order boundary value problems. [PDF]

ScientificWorldJournal, 2014
Abd-Elhameed WM.
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