Definition:Inverse Cosecant/Complex/Arccosecant

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Definition

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

$\forall z \in \C_{\ne 0}: \map \arccsc z := \dfrac 1 i \, \map \Ln {\dfrac {i + \sqrt {z^2 - 1} } z}$

where:

$\Ln$ denotes the principal branch of the complex natural logarithm
$\sqrt {z^2 - 1}$ denotes the principal square root of $z^2 - 1$.


Also denoted as

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

  • $\arccsc$
  • $\operatorname {arccosec}$
  • $\operatorname {acosec}$
  • $\operatorname {acsc}$


Also see


Sources