cth

The hyperbolic cotangent is defined as coth z congruent (e^z + e^(-z))/(e^z - e^(-z)) = (e^(2z) + 1)/(e^(2z) - 1). The notation cth z is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram Language as Coth[z]. The hyperbolic cotangent satisfies the identity coth(z/2) - coth z = csch z, where csch z is the hyperbolic cosecant.

Bernoulli number | bipolar coordinates | bipolar cylindrical coordinates | cotangent | hyperbolic functions | hyperbolic tangent | inverse hyperbolic cotangent | Laplace's equation--toroidal coordinates | Lebesgue constants | prolate spheroidal coordinates | surface of revolution | toroidal coordinates | toroidal function