trapezoidal rule

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1: 7.22 Methods of Computation

… ►Additional references are Matta and Reichel (1971) for the application of the trapezoidal rule, for example, to the first of (7.7.2), and Gautschi (1970) and Cuyt et al. (2008) for continued fractions. …

2: 8.25 Methods of Computation

… ►See Allasia and Besenghi (1987b) for the numerical computation of $\mathrm{\Gamma }(a,z)$ from (8.6.4) by means of the trapezoidal rule. …

3: 3.5 Quadrature

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§3.5(i) Trapezoidal Rules

►The elementary trapezoidal rule is given by … ►The composite trapezoidal rule is … ►Similar results hold for the trapezoidal rule in the form … ►

Table 3.5.20: Composite trapezoidal rule for the integral (3.5.45) with $\lambda =10$.

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$h$		$\mathrm{erfc}\lambda$		$n$
…

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4: 9.17 Methods of Computation

… ►The trapezoidal rule (§3.5(i)) is then applied. …

5: Bibliography

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Numerical computation of Tricomi’s psi function by the trapezoidal rule. Computing 39 (3), pp. 271–279.

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External Links:

ISSN 0010-485X, Document, MathReview, ZentralBlatt

Referenced by:

§13.29(iii).

Encodings:

BibTeX

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Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule. Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.

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External Links:

ISSN 0373-1243, MathReview, ZentralBlatt

Referenced by:

§13.29(iii).

Encodings:

BibTeX

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Numerical calculation of incomplete gamma functions by the trapezoidal rule. Numer. Math. 50 (4), pp. 419–428.

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External Links:

ISSN 0029-599X, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§8.25(ii).

Encodings:

BibTeX

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Numerical Calculation of the Riemann Zeta Function and Generalizations by Means of the Trapezoidal Rule. In Numerical and Applied Mathematics, Part II (Paris, 1988), C. Brezinski (Ed.), IMACS Ann. Comput. Appl. Math., Vol. 1, pp. 467–472.

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External Links:

MathReview

Referenced by:

§25.18(i).

Encodings:

BibTeX

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6: 13.29 Methods of Computation

… ►In Allasia and Besenghi (1991) and Allasia and Besenghi (1987a) the high accuracy of the trapezoidal rule for the computation of Kummer functions is described. …

7: 3.4 Differentiation

… ►The integral on the right-hand side can be approximated by the composite trapezoidal rule (3.5.2). … ►As explained in §§3.5(i) and 3.5(ix) the composite trapezoidal rule can be very efficient for computing integrals with analytic periodic integrands. …