Definition:Inverse Cotangent/Complex/Arccotangent

Definition

The principal branch of the complex inverse cotangent function is defined as:

$\map \arccot z := \dfrac 1 {2 i} \, \map \Ln {\dfrac {z + i} {z - i} }$

where $\Ln$ denotes the principal branch of the complex natural logarithm.

Symbol

The symbol used to denote the arccotangent function is variously seen as follows:

arccot

The usual symbol used on $\mathsf{Pr} \infty \mathsf{fWiki}$ to denote the arccotangent function is $\arccot$.

acot

A variant symbol used to denote the arccotangent function is $\operatorname {acot}$.

actn

A variant symbol used to denote the arccotangent function is $\operatorname {actn}$.

Also see

• Derivation of Complex Arctangent from Inverse Cotangent Multifunction

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $7$