The tanhc function is defined, by analogy with the tanc function, for complex numbers 
with 
by
 |
(1)
|
For 
in this domain, its derivative
is
 |
(2)
|
At the origin, 
. The indefinite
integral can apparently not be done in closed form
in terms of conventionally defined functions.
For real numbers 
, 
,
with equality iff 
. Its positive inflection
point is at 
(OEIS A133919), the unique root 
of
 |
(3)
|
The other real inflection point is its negative.
It has a unique real fixed point at 0.82242927726... (OEIS A133918).
