gives the inverse hyperbolic cotangent of the complex number .
- 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 .
- ArcCoth can be used with CenteredInterval objects. »
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.
Examplesopen allclose all
Basic Examples (6)
Asymptotic expansion at Infinity:
Numerical Evaluation (7)
Evaluate ArcCoth efficiently at high precision:
ArcCoth can deal with real‐valued intervals:
ArcCoth threads elementwise over lists and matrices:
Specific Values (5)
Plot the ArcCoth function:
Function Properties (11)
ArcCoth is defined for all real values except from the interval :
ArcCoth achieves all real values except 0:
ArcCoth is an odd function:
ArcCoth is not an analytic function:
ArcCoth is neither non-decreasing nor non-increasing:
ArcCoth is injective:
ArcCoth is not surjective:
ArcCoth is neither non-negative nor non-positive:
ArcCoth is neither convex nor concave:
Series Expansions (4)
Function Identities and Simplifications (3)
Branch cuts of ArcCoth:
Wolfram Research (1988), ArcCoth, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcCoth.html (updated 13).
Wolfram Language. 1988. "ArcCoth." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 13. https://reference.wolfram.com/language/ref/ArcCoth.html.
Wolfram Language. (1988). ArcCoth. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcCoth.html