This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Csch

 Csch[z]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:
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 Scope   (11)
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:
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:
 Applications   (2)
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:
Integrals:
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: