DLMF:

Digital Library of Mathematical Functions

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4 Elementary Functions Logarithm, Exponential, Powers 4.3 Graphics 4.3 Graphics 4.4 Special Values and Limits

Figure 4.3.2 (See in context.)

See accompanying text

(i)

-plane

(ii)

-plane

	A	B	C	$\overline{\mathrm{C}}$	D	$\overline{\mathrm{D}}$	E	$\overline{\mathrm{E}}$	F
	0		$r+i\pi$	$r-i\pi$	$i\pi$	$-i\pi$	$-r+i\pi$	$-r-i\pi$
	1	$e^{r}$	$-e^{r}+i0$	$-e^{r}-i0$			$-e^{{-r}}+i0$	$-e^{{-r}}-i0$	$e^{{-r}}$

Figure 4.3.2: Conformal mapping of exponential and logarithm. $w=e^{z}$ , $z=\mathop{\ln\/}\nolimits w$ .

Annotations:

Symbols:: : base of exponential function, $\mathop{\ln\/}\nolimits z$ : principal branch of logarithm function, : complex variable, : mapping and : real parameter
Permalink:: http://dlmf.nist.gov/4.3.F2.mag
Encodings:: Magnified png, pdf

© 2010–2013 NIST / Privacy Policy / Disclaimer / Feedback; Version 1.0.6; Release date 2013-05-06 Math-Image version (See MathML) . A Printed Companionis available. 4.3 Graphics 4.4 Special Values and Limits