Hyperbolic secant and hyperbolic cosecant
The hyperbolic cosecant (csch) and hyperbolic secant (six) functions are hyperbolic functions . They result from the reciprocal of the hyperbolic sine or hyperbolic cosine .
Definitions
properties
Hyperbolic secant | Hyperbolic cosecan | |
---|---|---|
Domain of definition | ||
Range of values | ||
periodicity | no | no |
monotony |
strictly monotonically increasing strictly monotonically decreasing
|
strictly monotonically falling strictly monotonically falling
|
Symmetries | Mirror symmetry to the y-axis | Point symmetry to the coordinate origin Axial symmetry to y = |
asymptote | For | For |
zeropoint | no | no |
Jump points | no | no |
Poles | no | |
Extremes | Maximum at x = 0 | no |
Turning points | no |
Inverse functions
The inverse functions are the corresponding area functions :
Derivatives
Integrals
Series developments
Complex argument
See also
Web links
- Eric W. Weisstein : Hyperbolic Cosecant . In: MathWorld (English).