naginterfaces.library.specfun.arcsinh

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

arcsinh returns the value of the inverse hyperbolic sine, .

For full information please refer to the NAG Library document for s11ab

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/s/s11abf.html

Parameters
xfloat

The argument of the function.

Returns
ashxfloat

The value of the inverse hyperbolic sine, .

Notes

arcsinh calculates an approximate value for the inverse hyperbolic sine of its argument, .

For it is based on the Chebyshev expansion

For it uses the fact that

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