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On Chebyshev quadrature for ultraspherical weight functions

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Abstract

It is well-known that for the ultraspherical weight function (1-x2)λ-1/2 there exist no Chebyshev quadrature formulae in the strict sense having n nodes, where n is sufficiently large and λ>0, whereas on the other hand for λ=0 every Gaussian quadrature formulae is a Chebyshev formula in the strict sense. In this paper we study the open question of Chebyshev quadrature for λ <0. It is shown that there exists no Chebyshev quadrature formula in the strict sense having more than two nodes for λ≤λ0=-.30056... (for definition of λ0 see (1.8) below). Moreover, results are obtained for Chebyshev-type formulae and Chebyshev formulae of closed type. For the remaining values of λ (λ0<λ<0) numerical results are given.

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  1. Institut für Angewandte Mathematik, Technische Universität Braunschweig, D-3300, Braunschweig, FRG

    K. -J. Förster

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Förster, K.J. On Chebyshev quadrature for ultraspherical weight functions. Calcolo 23, 355–381 (1986). https://doi.org/10.1007/BF02576117

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