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1: Bibliography X
  • H. Xiao, V. Rokhlin, and N. Yarvin (2001) Prolate spheroidal wavefunctions, quadrature and interpolation. Inverse Problems 17 (4), pp. 805–838.
  • 2: 3.5 Quadrature
    §3.5 Quadrature
    §3.5(iv) Interpolatory Quadrature Rules
    §3.5(v) Gauss Quadrature
    §3.5(viii) Complex Gauss Quadrature
    3: 18.38 Mathematical Applications
    Classical OP’s play a fundamental role in Gaussian quadrature. If the nodes in a quadrature formula with a positive weight function are chosen to be the zeros of the n th degree OP with the same weight function, and the interval of orthogonality is the same as the integration range, then the weights in the quadrature formula can be chosen in such a way that the formula is exact for all polynomials of degree not exceeding 2 n - 1 . …
    4: 5.21 Methods of Computation
    Another approach is to apply numerical quadrature3.5) to the integral (5.9.2), using paths of steepest descent for the contour. …
    5: 8.25 Methods of Computation
    §8.25(ii) Quadrature
    6: 14.32 Methods of Computation
  • Quadrature3.5) of the integral representations given in §§14.12, 14.19(iii), 14.20(iv), and 14.25; see Segura and Gil (1999) and Gil et al. (2000).

  • 7: 35.10 Methods of Computation
    Other methods include numerical quadrature applied to double and multiple integral representations. …
    8: 9.17 Methods of Computation
    For details, including the application of a generalized form of Gaussian quadrature, see Gordon (1969, Appendix A) and Schulten et al. (1979). … The second method is to apply generalized Gauss–Laguerre quadrature3.5(v)) to the integral (9.5.8). … For quadrature methods for Scorer functions see Gil et al. (2001), Lee (1980), and Gordon (1970, Appendix A); but see also Gautschi (1983). …
    9: 31.8 Solutions via Quadratures
    §31.8 Solutions via Quadratures
    the Hermite–Darboux method (see Whittaker and Watson (1927, pp. 570–572)) can be applied to construct solutions of (31.2.1) expressed in quadratures, as follows. …
    10: 11.13 Methods of Computation
    §11.13(iii) Quadrature