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Cosh

Cosh[z]
gives the hyperbolic cosine of z.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • .
  • For certain special arguments, Cosh automatically evaluates to exact values.
  • Cosh can be evaluated to arbitrary numerical precision.
  • Cosh automatically threads over lists.
Evaluate numerically:
Evaluate numerically:
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Cosh can take complex number inputs:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Cosh threads element-wise over lists and matrices:
Simple exact values are generated automatically:
Convert multiple-angle expressions:
Convert sums of hyperbolic functions to products:
Expand assuming real variables:
Convert to exponentials:
TraditionalForm formatting:
Cosh can deal with real-valued intervals:
Infinite arguments give symbolic results:
Cosh can be applied to power series:
Draw a hyperbola:
Build rotation matrix in hyperbolic space from infinitesimal transformations:
Relativistic boost matrix:
The matrix is orthogonal with respect to the Minkowski metric:
Construct a relativistic coordinate transformation for rapidity :
Nonrelativistic limit:
Special solution of the sine-Gordon equation:
Check the solution:
Pythagorean theorem in hyperbolic geometry:
The small limit gives the ordinary Pythagorean theorem:
Basic parity and periodicity properties of Cosh get automatically applied:
Expressions containing hyperbolic functions do not automatically simplify:
Compose with inverse functions:
Solve a hyperbolic equation:
Numerically find a root of a transcendental equation:
Reduce a hyperbolic equation:
Integrals:
Integral transforms:
Cosh appears in special cases of many mathematical functions:
Cosh is a numeric function:
Machine-precision input is insufficient to give a correct answer:
With exact input, the answer is correct:
A larger setting for $MaxExtraPrecision can be needed:
Machine-number inputs can give high-precision results:
No power series exists at infinity, where Cosh has an essential singularity:
In traditional form, parentheses are needed around the argument:
Nested hyperbolic cosine over the complex plane:
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