Positivity of the weights of extended Gauss-Legendre quadrature rules

Positivity of the weights of extended Gauss-Legendre quadrature rules
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by Giovanni Monegato PDF

Math. Comp. 32 (1978), 243-245 Request permission

We show that the weights of extended Gauss-Legendre quadrature rules are all positive.

References

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Giovanni Monegato, A note on extended Gaussian quadrature rules, Math. Comp. 30 (1976), no. 136, 812–817. MR 440878, DOI 10.1090/S0025-5718-1976-0440878-3
Robert Piessens and Maria Branders, A note on the optimal addition of abscissas to quadrature formulas of Gauss and Lobatto type, Math. Comp. 28 (1974), 135–139; supplement, ibid. 28 (1974), 344–347. MR 343552, DOI 10.1090/S0025-5718-1974-0343552-5
G. Szegö, Über gewisse orthogonale Polynome, die zu einer oszillierenden Belegungsfunktion gehören, Math. Ann. 110 (1935), no. 1, 501–513 (German). MR 1512952, DOI 10.1007/BF01448041

Orthogonal Polynomials