# numerical inversion

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## 1—10 of 35 matching pages

##### 1: 8.25 Methods of Computation

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►A numerical inversion procedure is also given for calculating the value of $x$ (with 10S accuracy), when $a$ and $P(a,x)$ are specified, based on Newton’s rule (§3.8(ii)).
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##### 2: Bibliography E

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The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature.
J. Comput. Appl. Math. 61 (1), pp. 43–72.
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##### 3: 3.11 Approximation Techniques

##### 4: 3.5 Quadrature

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###### Example. Laplace Transform Inversion

… ►A special case is the rule for Hilbert transforms (§1.14(v)): …##### 5: 4.45 Methods of Computation

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4.45.8
$$2\mathrm{arctan}\frac{x}{1+{(1+{x}^{2})}^{1/2}}=\mathrm{arctan}x,$$
$$.

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4.45.9
$${x}_{n}=\frac{{x}_{n-1}}{1+{(1+{x}_{n-1}^{2})}^{1/2}},$$
$n=1,2,3,\mathrm{\dots}$,

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##### 6: Bibliography S

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Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms.
Math. Tables Aids Comput. 9 (52), pp. 164–177.
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##### 7: Brian D. Sleeman

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►Sleeman has published numerous papers in applied analysis, multiparameter spectral theory, direct and inverse scattering theory, and mathematical medicine.
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##### 8: 4.46 Tables

###### §4.46 Tables

►Extensive numerical tables of all the elementary functions for real values of their arguments appear in Abramowitz and Stegun (1964, Chapter 4). …##### 9: Errata

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Equations (4.45.8), (4.45.9)
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These equations have been rewritten to improve the numerical computation of $\mathrm{arctan}x$.