ArcSech

ArcSech[z]

gives the inverse hyperbolic secant of the complex number .

Details

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

Background & Context

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

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 expansions:

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Scope  (5)

Generalizations & Extensions  (2)

Applications  (1)

Properties & Relations  (4)

See Also

Sech  ArcCsch  ArcSec  TrigToExp  TrigExpand

Tutorials

Introduced in 1988
(1.0)