4 Elementary FunctionsLogarithm, Exponential, Powers4.3 Graphics4.3 Graphics4.4 Special Values and Limits

(i) $z$-plane

(ii) $w$-plane

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

ⓘ

Annotations:

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\overline{z}$: complex conjugate, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $\ln z$: principal branch of logarithm function, $z$: complex variable, $w$: mapping and $r$: real parameter

Permalink:

http://dlmf.nist.gov/4.3.F2.mag

Encodings:

Magnified png, pdf

See also:

Annotations for §4.3 and Ch.4

4.3 Graphics4.4 Special Values and Limits

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