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based on Chebyshev points

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1: 3.3 Interpolation
§3.3(vi) Other Interpolation Methods
For Hermite interpolation, trigonometric interpolation, spline interpolation, rational interpolation (by using continued fractions), interpolation based on Chebyshev points, and bivariate interpolation, see Bulirsch and Rutishauser (1968), Davis (1975, pp. 27–31), and Mason and Handscomb (2003, Chapter 6). …
2: Bibliography B
  • P. Baldwin (1991) Coefficient functions for an inhomogeneous turning-point problem. Mathematika 38 (2), pp. 217–238.
  • R. Barakat (1961) Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials. Math. Comp. 15 (73), pp. 7–11.
  • J. M. Blair, C. A. Edwards, and J. H. Johnson (1976) Rational Chebyshev approximations for the inverse of the error function. Math. Comp. 30 (136), pp. 827–830.
  • J. M. Blair, C. A. Edwards, and J. H. Johnson (1978) Rational Chebyshev approximations for the Bickley functions K i n ( x ) . Math. Comp. 32 (143), pp. 876–886.
  • N. Bleistein (1966) Uniform asymptotic expansions of integrals with stationary point near algebraic singularity. Comm. Pure Appl. Math. 19, pp. 353–370.
  • 3: Bibliography S
  • L. Schoenfeld (1976) Sharper bounds for the Chebyshev functions θ ( x ) and ψ ( x ) . II. Math. Comp. 30 (134), pp. 337–360.
  • J. L. Schonfelder (1978) Chebyshev expansions for the error and related functions. Math. Comp. 32 (144), pp. 1232–1240.
  • J. L. Schonfelder (1980) Very high accuracy Chebyshev expansions for the basic trigonometric functions. Math. Comp. 34 (149), pp. 237–244.
  • J. Segura (2002) The zeros of special functions from a fixed point method. SIAM J. Numer. Anal. 40 (1), pp. 114–133.
  • P. N. Shivakumar and J. Xue (1999) On the double points of a Mathieu equation. J. Comput. Appl. Math. 107 (1), pp. 111–125.
  • 4: 18.3 Definitions
    §18.3 Definitions
    This table also includes the following special cases of Jacobi polynomials: ultraspherical, Chebyshev, and Legendre. …
    Chebyshev
    In addition to the orthogonal property given by Table 18.3.1, the Chebyshev polynomials T n ( x ) , n = 0 , 1 , , N , are orthogonal on the discrete point set comprising the zeros x N + 1 , n , n = 1 , 2 , , N + 1 , of T N + 1 ( x ) : … Formula (18.3.1) can be understood as a Gauss-Chebyshev quadrature, see (3.5.22), (3.5.23). …
    5: 3.5 Quadrature
    For the latter a = 1 , b = 1 , and the nodes x k are the extrema of the Chebyshev polynomial T n ( x ) 3.11(ii) and §18.3). …
    Gauss–Chebyshev Formula
    To avoid cancellation we try to deform the path to pass through a saddle point in such a way that the maximum contribution of the integrand is derived from the neighborhood of the saddle point. … with saddle point at t = 1 , and when c = 1 the vertical path intersects the real axis at the saddle point. …