# Functions dependent on a greater number of parameters

hello :)

let's look at the following functions:

Langevin function L(x)=ctgh(x)-1/x
Brillouin function B(x)=f(x J); when J→∞, then B(x)=L(x)

to which I have the following questions:

- how was the Brillouin function B(x)=f(x,J) developed?
- are there other functions with the properties of the function B - dependent on a greater number of parameters, that would allow to model more objects?

I would appreciate any help, so please do ;) greets!

$$B_J(x)=\frac{2J+1}{2J}\coth (\frac{2J+1}{2J}x)-\frac{1}{2J}\coth (\frac{1}{2J}x)$$