Summary
It is well known that the Chebyshev weight function (1−x 2)−1/2 is the only weight function (up to a linear transformation) for which then point Gauss quadrature formula has equal weights for alln∈ℕ. In this paper we describe all weight functions for which thenm point Gauss quadrature formula has equal weights for alln∈ℕ, wherem∈ℕ is fixed.
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References
Brass, H.: Quadraturverfahren. Göttingen: Vanderhoeck und Ruprecht 1977
Gautschi, W.: Advances in Chebyshev quadrature. Lect. Notes Math.506, 100–121 (1976)
Gautschi, W.: On some polynomials of interest in theoretical chemistry. BIT24, 473–483 (1984)
Hildebrand, F.: Introduction to numerical analysis. New York: Mc Graw-Hill 1974
Levinson, N.: Simplified treatment of integrals of Cauchy type, the Hilbert Problem and singular integral equations. SIAM Rev.7, 474–502 (1965)
Peherstorfer, F.: On Tchebycheff polynomials on disjoint intervals. Colloq. Math. Soc. BOLYAI, 49. HAAR Mem. Conf, Budapest 1985, pp. 737–751
Peherstorfer, F.: Weight functions which admit Tchebycheff quadrature. Bull. Austral. Math. Soc.26, 29–37 (1982)
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Peherstorfer, F. On Gauss quadrature formulas with equal weights. Numer. Math. 52, 317–327 (1987). https://doi.org/10.1007/BF01398882
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DOI: https://doi.org/10.1007/BF01398882