Clenshaw algorithm

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11: Bibliography L

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Algorithm 537: Characteristic values of Mathieu’s differential equation. ACM Trans. Math. Software 5 (1), pp. 112–117.

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ISSN 0098-3500, Document, GAMS (module 537; package TOMS)

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2nd item, 2nd item.

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Numerical evaluation of integrals containing a spherical Bessel function by product integration. J. Math. Phys. 22 (7), pp. 1399–1413.

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ISSN 0022-2488, Document, MathReview (C. W. Clenshaw), ZentralBlatt

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§10.74(vii).

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Algorithm 244: Fresnel integrals. Comm. ACM 7 (11), pp. 660–661.

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Notes:

Includes Algol program, maximum accuracy 12D.

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ISSN 0001-0782, Document

Referenced by:

§7.25(iv).

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Algorithms for rational approximations for a confluent hypergeometric function. Utilitas Math. 11, pp. 123–151.

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External Links:

MathReview (F. Gotze), ZentralBlatt

Referenced by:

§13.31(iii).

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Algorithms for the Computation of Mathematical Functions. Academic Press, New York.

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External Links:

MathReview (Gh. Adam)

Referenced by:

§16.26.

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12: 3.5 Quadrature

… ►If we add $-1$ and $1$ to this set of $x_k$, then the resulting closed formula is the frequently-used Clenshaw–Curtis formula, whose weights are positive and given by … ►For further information, see Mason and Handscomb (2003, Chapter 8), Davis and Rabinowitz (1984, pp. 74–92), and Clenshaw and Curtis (1960). ►For detailed comparisons of the Clenshaw–Curtis formula with Gauss quadrature (§3.5(v)), see Trefethen (2008, 2011). … ► …