naginterfaces.library.specfun.arccosh

naginterfaces.library.specfun.arccosh(x)[source]

arccosh returns the value of the inverse hyperbolic cosine, . The result is in the principal positive branch.

For full information please refer to the NAG Library document for s11ac

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s11acf.html

Parameters
xfloat

The argument of the function.

Returns
achxfloat

The value of the inverse hyperbolic cosine, .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

The function has been called with an argument less than , for which is not defined.

Notes

arccosh calculates an approximate value for the inverse hyperbolic cosine, . It is based on the relation

This form is used directly for , where , and the machine uses approximately decimal place arithmetic.

For , is equal to to within the accuracy of the machine and hence we can guard against premature overflow and, without loss of accuracy, calculate

References

NIST Digital Library of Mathematical Functions