Results 91 to 100 of about 909 (183)

The Zeros of Orthogonal Polynomials for Jacobi-Exponential Weights

Abstract and Applied Analysis, 2012
This paper gives the estimates of the zeros of orthogonal polynomials for Jacobi-exponential weights.
Rong Liu, Ying Guang Shi
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A Bochner Theorem for Dunkl Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2011
We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions.
Luc Vinet, Alexei Zhedanov
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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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Darboux transformation of symmetric Jacobi matrices and Toda lattices

Frontiers in Applied Mathematics and Statistics
Let J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively.
Ivan Kovalyov, Oleksandra Levina
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A numerical method based on the shifted Jacobi polynomials for a class of tempered fractional quadratic integro-differential equations

Results in Applied Mathematics
This paper introduces a new class of tempered fractional quadratic integro-differential equations using the Caputo fractional derivative. The existence and uniqueness of solutions to these equations are analyzed.
P. Senfiazad, M.H. Heydari, M. Bayram, D. Baleanu   +3 more
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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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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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Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms. [PDF]

Philos Trans A Math Phys Eng Sci
Minenkova A, Mograby G, Zhan H.
europepmc   +1 more source