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11: 11.13 Methods of Computation

… ►For simple and effective approximations to ${𝐇}_0\left(z\right)$ and ${𝐇}_1\left(z\right)$ see Aarts and Janssen (2016). …

12: 24.19 Methods of Computation

… ►For example, the tangent numbers $T_n$ can be generated by simple recurrence relations obtained from (24.15.3), then (24.15.4) is applied. …

13: Bibliography J

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Simple-periodic and Non-periodic Lamé Functions. Mathematical Centre Tracts, No. 72, Mathematisch Centrum, Amsterdam.

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External Links:

ISBN 90-6196-130-0, MathReview (V. P. Madan)

Referenced by:

§29.1, §29.1, §29.18(i), §29.19(i), §29.20(i), §29.20(i), §29.22(ii), §29.3(v), §29.6(i), §29.6(ii), §29.6(iii), §29.6(iv), Ch.29, Notations L, Notations L, Notations L, Notations L.

Encodings:

BibTeX

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On the simple cubic lattice Green function. Philos. Trans. Roy. Soc. London Ser. A 273, pp. 583–610.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§31.17(ii).

Encodings:

BibTeX

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14: Bibliography N

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Uniform Asymptotic Approximations of Solutions of Second-order Linear Differential Equations, with a Coalescing Simple Turning Point and Simple Pole. Ph.D. Thesis, University of Maryland, College Park, MD.

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Referenced by:

§2.8(vi).

Encodings:

BibTeX

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15: 1.10 Functions of a Complex Variable

… ►When $m=1$ the zero is simple. … ►A cut domain is one from which the points on finitely many nonintersecting simple contours (§1.9(iii)) have been removed. …(Or more generally, a simple contour that starts at the center and terminates on the boundary.) … ►is analytic in $ℂ$, except for simple poles at $z=z_n$ of residue $a_n$. …

16: 1.9 Calculus of a Complex Variable

… ►A simple closed contour is a simple contour, except that $z(a)=z(b)$. … ►Any simple closed contour $C$ divides $ℂ$ into two open domains that have $C$ as common boundary. … ►If $f(z)$ is continuous within and on a simple closed contour $C$ and analytic within $C$, then … ►If $f(z)$ is continuous within and on a simple closed contour $C$ and analytic within $C$, and if $z_0$ is a point within $C$, then …

17: Bibliography Z

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Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function. ACM Trans. Math. Softw. 44 (2), pp. 22:1–22:9.

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External Links:

ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

4th item, §7.25(iii).

Encodings:

BibTeX

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18: 9.19 Approximations

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Martín et al. (1992) provides two simple formulas for approximating $\mathrm{Ai}\left(x\right)$ to graphical accuracy, one for , the other for .

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19: 10.58 Zeros

… ►However, there are no simple relations that connect the zeros of the derivatives. …

20: 1.4 Calculus of One Variable

… ►A simple discontinuity of $f(x)$ at $x=c$ occurs when $f(c+)$ and $f(c-)$ exist, but $f(c+)\ne f(c-)$. If $f(x)$ is continuous on an interval $I$ save for a finite number of simple discontinuities, then $f(x)$ is piecewise (or sectionally) continuous on $I$. For an example, see Figure 1.4.1 …