The exponential funtion is defined, for all objects for which this makes
sense, as the power series ,
with
The hyperbolic functions are defined as power series which can be computed (for reals, complex, quaternions and octonions) as: Hyperbolic cosine: Hyperbolic sine: Hyperbolic tangent:
The hyperbolic sine is one to one on the set of real numbers, with range
the full set of reals, while the hyperbolic tangent is also one to one
on the set of real numbers but with range The inverse of the hyperbolic tangent is called the Argument hyperbolic tangent, and can be computed as .
The inverse of the hyperbolic sine is called the Argument hyperbolic sine,
and can be computed (for The inverse of the hyperbolic cosine is called the Argument hyperbolic cosine, and can be computed as . |