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Orthogonal Polynomials with Respect to Modified Jacobi Weight and Corresponding Quadrature Rules of Gaussian Type
Published online by Cambridge University Press: 28 May 2015
Abstract
In this paper we consider polynomials orthogonal with respect to the linear functional defined on the space of all algebraic polynomials by
where α,β> -1/2 are real numbers such that ℓ = |β - α| is a positive integer, and ζ∈ R{0}. We prove the existence of such orthogonal polynomials for some pairs of α and ζ and for all nonnegative integers ℓ. For such orthogonal polynomials we derive three-term recurrence relations and also some differential-difference relations. For such orthogonal polynomials the corresponding quadrature rules of Gaussian type are considered. Also, some numerical examples are included.
Keywords
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- Research Article
- Information
- Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 4 , November 2011 , pp. 478 - 488
- Copyright
- Copyright © Global Science Press Limited 2011