# ArcCoth

ArcCoth[z]

gives the inverse hyperbolic cotangent of the complex number .

# Details • Mathematical function, suitable for both symbolic and numerical manipulation.
• For certain special arguments, ArcCoth automatically evaluates to exact values.
• ArcCoth can be evaluated to arbitrary numerical precision.
• ArcCoth automatically threads over lists.
• ArcCoth[z] has a branch cut discontinuity in the complex plane running from to .

# Background & Context

• ArcCoth is the inverse hyperbolic cotangent function. For a real number , ArcCoth[x] represents the hyperbolic angle measure such that .
• ArcCoth automatically threads over lists. For certain special arguments, ArcCoth automatically evaluates to exact values. When given exact numeric expressions as arguments, ArcCoth may be evaluated to arbitrary numeric precision. Operations useful for manipulation of symbolic expressions involving ArcCoth include FunctionExpand, TrigToExp, TrigExpand, Simplify, and FullSimplify.
• ArcCoth is defined for complex argument by . ArcCoth[z] has a branch cut discontinuity in the complex plane.
• Related mathematical functions include ArcTanh, Coth, and ArcCot.

# Examples

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## Basic Examples(3)

Evaluate numerically:

 In:= Out= Plot over a subset of the reals:

 In:= Out= Series expansion:

 In:= Out= ## Properties & Relations(1)

Introduced in 1988
(1.0)