Gudermannian function
From Wikipedia, the free encyclopedia
marked in gray.)The Gudermannian function, named after Christoph Gudermann (1798 - 1852), relates the circular and hyperbolic trigonometric functions without resorting to complex numbers.
It is defined by
The following identities also hold:
The inverse Gudermannian function is given by
The derivatives of the Gudermannian and its inverse are
[edit] See also
- Hyperbolic secant distribution
- Mercator projection
- Tangent half-angle formula
- Tractrix
- Trigonometric identity
[edit] References
- CRC Handbook of Mathematical Sciences 5th ed. pp 323-5.
- Eric W. Weisstein, Gudermannian Function at MathWorld.
