gives the inverse hyperbolic cosecant of the complex number .
- 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 .
- ArcCsch can be used with Interval and CenteredInterval objects. »
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.
Examplesopen allclose all
Basic Examples (6)
Asymptotic expansion at Infinity:
Numerical Evaluation (6)
Evaluate ArcCsch efficiently at high precision:
ArcCsch threads elementwise over lists and matrices:
Specific Values (4)
Plot the ArcCsch function:
Function Properties (11)
ArcCsch is defined for all real values except 0:
ArcCsch achieves all real values except 0:
ArcCsch is an odd function:
ArcCsch has the mirror property :
ArcCsch is not an analytic function:
ArcCsch is neither non-decreasing nor non-increasing:
ArcCsch is injective:
ArcCsch is neither non-negative nor non-positive:
ArcCsch is neither convex nor concave:
Series Expansions (3)
Function Identities and Simplifications (3)
Branch cut structure of ArcCsch runs along the imaginary axis:
Wolfram Research (1988), ArcCsch, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcCsch.html (updated 2021).
Wolfram Language. 1988. "ArcCsch." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/ArcCsch.html.
Wolfram Language. (1988). ArcCsch. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcCsch.html