Gudermannian function
The
Gudermannian function relates the
circular
and
hyperbolic trigonometric functions without resorting to
complex numbers. It is defined by
The following identities follow:
-
-
-
-
-
The inverse,
is the core of the
Mercator projection.
The following identities also hold:
Ref: CRC
Handbook of Mathematical Sciences 5th ed. pp323–5