half argument

SearchAdvancedHelp

(0.001 seconds)

21—22 of 22 matching pages

21: 4.23 Inverse Trigonometric Functions

… ►Graphs of the principal values for real arguments are given in §4.15. This section also includes conformal mappings, and surface plots for complex arguments. … ►

4.23.24 $$\arccos x=\mp \mathrm{i}\ln \left({(x^2-1)}^{1/2}+x\right),$$ $x\in [1,\mathrm{\infty })$,

ⓘ

Symbols:

$[a,b)$: half-closed interval, $\in$: element of, $\mathrm{i}$: imaginary unit, $\arccos z$: arccosine function, $\ln z$: principal branch of logarithm function and $x$: real variable

Permalink:

http://dlmf.nist.gov/4.23.E24

Encodings:

pMML, png, TeX

See also:

Annotations for §4.23(iv), §4.23(iv), §4.23 and Ch.4

►

4.23.25 $$\arccos x=\pi \mp \mathrm{i}\ln \left({(x^2-1)}^{1/2}-x\right),$$ $x\in (-\mathrm{\infty },-1]$,

ⓘ

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\in$: element of, $\mathrm{i}$: imaginary unit, $\arccos z$: arccosine function, $\ln z$: principal branch of logarithm function, $(a,b]$: half-closed interval and $x$: real variable

Permalink:

http://dlmf.nist.gov/4.23.E25

Encodings:

pMML, png, TeX

See also:

Annotations for §4.23(iv), §4.23(iv), §4.23 and Ch.4

… ►

4.23.26 $$\arctan z=\frac{\mathrm{i}}{2}\ln \left(\frac{\mathrm{i}+z}{\mathrm{i}-z}\right),$$ $z/\mathrm{i}\in ℂ\setminus (-\mathrm{\infty },-1]\cup [1,\mathrm{\infty })$;

ⓘ

Symbols:

$[a,b)$: half-closed interval, $ℂ$: complex plane, $\in$: element of, $\mathrm{i}$: imaginary unit, $\arctan z$: arctangent function, $\ln z$: principal branch of logarithm function, $(a,b]$: half-closed interval, $\setminus$: set subtraction, $\cup$: union and $z$: complex variable

Referenced by:

§4.23(iv)

Permalink:

http://dlmf.nist.gov/4.23.E26

Encodings:

pMML, png, TeX

See also:

Annotations for §4.23(iv), §4.23(iv), §4.23 and Ch.4

…

22: 1.10 Functions of a Complex Variable

… ►Let $C$ be a simple closed contour consisting of a segment $\mathrm{𝐴𝐵}$ of the real axis and a contour in the upper half-plane joining the ends of $\mathrm{𝐴𝐵}$. … ►

Phase (or Argument) Principle

…