An asymptotic expansion for the weights of Gaussian quadrature formulae

Acta Mathematica Hungarica

Volumn 70, Issue 1-2, 1996, Pages 89-100

  Petras, K ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030545275     PISSN: 02365294     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00113915     Document Type: Article

References (7)

1. M. Abramowitz and I.A. Stegun (eds.), Handbook of Mathematical Functions, 7th printing, Dover (New York, 1970).
2. K.-J. Förster and K. Petras, On estimates for the weights in Gaussian quadrature in the ultraspherical case, Math. Comp., 55 (1990), 243-264.
3. K.-J. Förster and K. Petras, On the zeros of ultraspherical polynomials and Bessel functions, in: Orthogonal Polynomials and their Applications (C. Brezinski, L. Gori and A. Ronveaux, eds.), IMACS Ann. Comput. Appl. Math. Vol. 9 (1991), pp. 257-262.
4. K.-J. Förster and K. Petras, On the variance of Gaussian quadrature formulae in the ultraspherical case. Submitted.
5. C. L. Frenzen and R. Wong, A uniform asymptotic expansion of the Jacobi polynomials with error bounds, Can. J. Math., 37 (1985), 979-1007.
6. L. Gatteschi, Uniform approximation of Chistoffel numbers for Jacobi weight, in: Numerical Integration III (H. Braß and G. Hämmerlin, eds.), Intern. Ser. Numer. Math. Vol. 85, Birkhäuser (Basel, 1988), pp. 49-59.
7. G. Szegö, Orthogonal Polynomials, AMS Colloq. Publ. Vol. 23 (Providence, 1939).