Experimental Mathematics Involving Orthogonal Polynomials

Walter Gautschi ()
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Walter Gautschi: Purdue University

A chapter in Approximation and Computation, 2010, pp 117-134 from Springer

Abstract: Abstract An account is given of computational work in support of conjectured inequalities for zeros of Jacobi polynomials, the sharpness of Bernstein’s inequality for Jacobi polynomials, and the positivity of certain quadrature formulae of Newton–Cotes, Gauss–Radau, and Gauss–Lobatto type. The use of symbolic computation is described for generating Gauss quadrature rules with exotic weight functions, specifically weight functions decaying super-exponentially at infinity, and weight functions densely oscillatory at zero.

Keywords: Weight Function; Orthogonal Polynomial; Quadrature Formula; Jacobi Polynomial; Large Zero (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-6594-3_9

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DOI: 10.1007/978-1-4419-6594-3_9

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