Defining the hyperbolic cosecant function
The hyperbolic cosecant function is an old mathematical function.
This function has a simple definition as the reciprocal to hyperbolic sine functions:
After comparison with the famous Euler formula for the sine function , it is easy to derive the following representation of the hyperbolic cosecant through the circular cosecant:
This formula allows the derivation of all the properties and formulas for the hyperbolic cosecant from the corresponding properties and formulas for the circular cosecant.