based on Chebyshev points

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1: 3.3 Interpolation

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§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

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Coefficient functions for an inhomogeneous turning-point problem. Mathematika 38 (2), pp. 217–238.

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External Links:

ISSN 0025-5793, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§2.8(iii).

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Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials. Math. Comp. 15 (73), pp. 7–11.

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External Links:

FullText, MathReview (J. C. P. Miller), ZentralBlatt

Referenced by:

§8.7.

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Rational Chebyshev approximations for the inverse of the error function. Math. Comp. 30 (136), pp. 827–830.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§7.17(iii), §7.17(iii).

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Rational Chebyshev approximations for the Bickley functions $K{i}_n(x)$ . Math. Comp. 32 (143), pp. 876–886.

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External Links:

ISSN 0025-5718, FullText, MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§10.76(iii).

Encodings:

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Uniform asymptotic expansions of integrals with stationary point near algebraic singularity. Comm. Pure Appl. Math. 19, pp. 353–370.

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External Links:

Document, MathReview (J. G. van der Corput), ZentralBlatt

Referenced by:

§2.3(v).

Encodings:

BibTeX

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3: Bibliography S

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Sharper bounds for the Chebyshev functions $\theta (x)$ and $\psi (x)$. II. Math. Comp. 30 (134), pp. 337–360.

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Notes:

For corrigendum see same journal v. 30 (1976), no. 136, p. 900

External Links:

FullText, Document, MathReview (R. P. Brent), ZentralBlatt

Referenced by:

§27.12.

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Chebyshev expansions for the error and related functions. Math. Comp. 32 (144), pp. 1232–1240.

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External Links:

FullText, Document, MathReview (L. Fox), ZentralBlatt

Referenced by:

3rd item.

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Very high accuracy Chebyshev expansions for the basic trigonometric functions. Math. Comp. 34 (149), pp. 237–244.

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External Links:

ISSN 0025-5718, FullText, Document, MathReview (Claude Carasso), ZentralBlatt

Referenced by:

§4.47(i).

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The zeros of special functions from a fixed point method. SIAM J. Numer. Anal. 40 (1), pp. 114–133.

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External Links:

ISSN 1095-7170, Document, MathReview, ZentralBlatt

Referenced by:

§3.8(v).

Encodings:

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On the double points of a Mathieu equation. J. Comput. Appl. Math. 107 (1), pp. 111–125.

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External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§28.7.

Encodings:

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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 $T_n\left(x\right)$, $n=0,1,\mathrm{\dots },N$, are orthogonal on the discrete point set comprising the zeros $x_{N+1,n},n=1,2,\mathrm{\dots },N+1$, of $T_{N+1}\left(x\right)$: … ►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 $T_n\left(x\right)$ (§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. …