naginterfaces.library.specfun.arctanh

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

arctanh returns the value of the inverse hyperbolic tangent, .

For full information please refer to the NAG Library document for s11aa

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s11aaf.html

Parameters
xfloat

The argument of the function.

Returns
athxfloat

The value of the inverse hyperbolic tangent, .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

The function has been called with an argument greater than or equal to in magnitude, for which is not defined.

Notes

arctanh calculates an approximate value for the inverse hyperbolic tangent of its argument, .

For it is based on the Chebyshev expansion

where , , .

For , it uses

For , the function fails as is undefined.

References

NIST Digital Library of Mathematical Functions