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
open allclose allBasic Examples (6)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Asymptotic expansion at Infinity:
Scope (36)
Numerical Evaluation (6)
Specific Values (5)
Visualization (3)
Function Properties (4)
ArcCoth is defined for all real values except from the interval :
ArcCoth achieves all real values except 0:
Function range for arguments from the complex domain:
ArcCoth is an odd function:
TraditionalForm formatting:
Integration (3)
Series Expansions (4)
Function Identities and Simplifications (3)
Function Representations (5)
Represent using ArcCoth:
Representation through inverse Jacobi functions:
ArcCoth is a special case of Hypergeometric2F1:
ArcCoth can be represented in terms of MeijerG:
ArcCoth can be represented as a DifferentialRoot:
Applications (1)
Branch cuts of ArcCoth:
Text
Wolfram Research (1988), ArcCoth, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcCoth.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 1988. "ArcCoth." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArcCoth.html.
APA
Wolfram Language. (1988). ArcCoth. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcCoth.html