hyperbolic function summary

hyperbolic function:  双曲函数

Standard algebraic expressions

 

Hyperbolic functions can be introduced via imaginary circular angles:

 

Useful relations

 

 

Inverse functions as logarithms

 

Derivatives

 

 

Standard integrals

 

 

Taylor series expressions

 

 

Identities

 

 

Relationship to the exponential function

 

 

Hyperbolic functions for complex numbers