Experimental Mathematics Involving Orthogonal Polynomials

  • Walter Gautschi
Part of the Springer Optimization and Its Applications book series (SOIA, volume 42)


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.


Weight Function Orthogonal Polynomial Quadrature Formula Jacobi Polynomial Large Zero 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Computer SciencesPurdue UniversityWest LafayetteUSA

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