# ArcCsch

ArcCsch[z]

gives the inverse hyperbolic cosecant of the complex number .

# Details

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

# Background & Context

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

# Examples

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## Basic Examples(3)

Evaluate numerically:

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Plot over a subset of the reals:

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Series expansion:

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