# absolute

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## 1—10 of 46 matching pages

##### 1: 19.38 Approximations
Minimax polynomial approximations (§3.11(i)) for $K\left(k\right)$ and $E\left(k\right)$ in terms of $m=k^{2}$ with $0\leq m<1$ can be found in Abramowitz and Stegun (1964, §17.3) with maximum absolute errors ranging from 4×10⁻⁵ to 2×10⁻⁸. Approximations of the same type for $K\left(k\right)$ and $E\left(k\right)$ for $0 are given in Cody (1965a) with maximum absolute errors ranging from 4×10⁻⁵ to 4×10⁻¹⁸. …
##### 2: 3.1 Arithmetics and Error Measures
The lower and upper bounds for the absolute values of the nonzero machine numbers are given by … Also in this arithmetic generalized precision can be defined, which includes absolute error and relative precision (§3.1(v)) as special cases. … If $x^{*}$ is an approximation to a real or complex number $x$, then the absolute error is
3.1.8 $\epsilon_{a}=\left|x^{*}-x\right|.$
3.1.9 $\epsilon_{r}=\left|\frac{x^{*}-x}{x}\right|=\frac{\epsilon_{a}}{\left|x\right|}.$
##### 3: 6.13 Zeros
$\operatorname{Ci}\left(x\right)$ and $\operatorname{si}\left(x\right)$ each have an infinite number of positive real zeros, which are denoted by $c_{k}$, $s_{k}$, respectively, arranged in ascending order of absolute value for $k=0,1,2,\dots$. …
##### 4: 23.16 Graphics
In Figures 23.16.2 and 23.16.3, height corresponds to the absolute value of the function and color to the phase. …
##### 5: 4.3 Graphics
In the graphics shown in this subsection height corresponds to the absolute value of the function and color to the phase. …
##### 6: 5.3 Graphics
In the graphics shown in this subsection, both the height and color correspond to the absolute value of the function. …
##### 7: 8.27 Approximations
• DiDonato (1978) gives a simple approximation for the function $F(p,x)=x^{-p}e^{x^{2}/2}\int_{x}^{\infty}e^{-t^{2}/2}t^{p}\,\mathrm{d}t$ (which is related to the incomplete gamma function by a change of variables) for real $p$ and large positive $x$. This takes the form $F(p,x)=4x/h(p,x)$, approximately, where $h(p,x)=3(x^{2}-p)+\sqrt{(x^{2}-p)^{2}+8(x^{2}+p)}$ and is shown to produce an absolute error $O\left(x^{-7}\right)$ as $x\to\infty$.

• ##### 8: 9.3 Graphics
In the graphics shown in this subsection, height corresponds to the absolute value of the function and color to the phase. …
##### 9: 14.22 Graphics
In the graphics shown in this section, height corresponds to the absolute value of the function and color to the phase. …
##### 10: 7.13 Zeros
$\operatorname{erf}z$ has a simple zero at $z=0$, and in the first quadrant of $\mathbb{C}$ there is an infinite set of zeros $z_{n}=x_{n}+iy_{n}$, $n=1,2,3,\dots$, arranged in order of increasing absolute value. … In the sector $\tfrac{1}{2}\pi<\operatorname{ph}z<\tfrac{3}{4}\pi$, $\operatorname{erfc}z$ has an infinite set of zeros $z_{n}=x_{n}+iy_{n}$, $n=1,2,3,\dots$, arranged in order of increasing absolute value. … In the first quadrant of $\mathbb{C}$ $C\left(z\right)$ has an infinite set of zeros $z_{n}=x_{n}+iy_{n}$, $n=1,2,3,\dots$, arranged in order of increasing absolute value. …