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21: 3.10 Continued Fractions

… ►We continue by means of the rhombus rule …

22: 1.6 Vectors and Vector-Valued Functions

… ►where $𝐧$ is the unit vector normal to $𝐚$ and $𝐛$ whose direction is determined by the right-hand rule; see Figure 1.6.1. ►

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Figure 1.6.1: Vector notation. Right-hand rule for cross products. Magnify

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23: 34.5 Basic Properties: $\mathit{6}j$ Symbol

… ►Equations (34.5.15) and (34.5.16) are the sum rules. They constitute addition theorems for the $\mathit{6}j$ symbol. …

24: 4.45 Methods of Computation

… ►For $x\in [-1/\mathrm{e},\mathrm{\infty })$ the principal branch $\mathrm{Wp}\left(x\right)$ can be computed by solving the defining equation $W{\mathrm{e}}^W=x$ numerically, for example, by Newton’s rule (§3.8(ii)). …

25: 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. …

26: 17.2 Calculus

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Product Rule

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Leibniz Rule

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27: Bibliography T

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The numerical computation of special functions by use of quadrature rules for saddle point integrals. II. Gamma functions, modified Bessel functions and parabolic cylinder functions. Report TW 183/78 Mathematisch Centrum, Amsterdam, Afdeling Toegepaste Wiskunde.

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Notes:

Algol procedures, maximum accuracy 14S.

External Links:

FullText, ZentralBlatt

Referenced by:

§12.21(ii).

Encodings:

BibTeX

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28: 3.11 Approximation Techniques

… ►The Padé approximants can be computed by Wynn’s cross rule. Any five approximants arranged in the Padé table as …

29: 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. …

30: Bibliography W

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Fast construction of the Fejér and Clenshaw-Curtis quadrature rules. BIT 46 (1), pp. 195–202.

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External Links:

ISSN 0006-3835, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.5(iv).

Encodings:

BibTeX

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