This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


gives the hyperbolic cosecant of z.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • .
  • For certain special arguments, Csch automatically evaluates to exact values.
  • Csch can be evaluated to arbitrary numerical precision.
  • Csch automatically threads over lists.
Evaluate numerically:
Evaluate numerically:
Click for copyable input
Click for copyable input
Click for copyable input
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Csch threads element-wise over lists and matrices:
Evaluate for complex arguments:
Simple exact values are generated automatically:
Convert multiple-angle expressions:
Find factors of decomposition:
Convert sums of hyperbolic functions to products:
Expand assuming real variables:
Convert to exponentials:
TraditionalForm formatting:
Csch can deal with real-valued intervals:
Infinite arguments give symbolic results:
Csch can be applied to power series:
Csch threads element-wise over sparse arrays as well as lists:
Plot absolute value over the complex plane:
Plot Poinsot's spirals:
Basic parity and periodicity properties of Csch get automatically applied:
Use Simplify and FullSimplify to simplify expressions containing Csch:
Use FunctionExpand to express special values in radicals:
Compose with inverse functions:
Solve a hyperbolic equation:
Numerically find a root of a transcendental equation:
Integral transforms:
Obtain Csch from sums, products, and differential equations:
Csch appears in special cases of special functions:
Csch is a numeric function:
Machine-precision input is insufficient to give a correct answer:
Use arbitrary-precision evaluation instead:
A larger setting for $MaxExtraPrecision can be needed:
The inverse of Csch evaluates to Sinh:
No power series exists at infinity, where Csch has an essential singularity:
In traditional form parentheses are needed around the argument:
Plot Csch at infinity:
New in 1 | Last modified in 3