# 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!

## Answers and Replies

Brillouin function describes magnetization of paramagnet.
## M=Ng\mu_B J B_J(x) ##
where ##N## is number of atoms per unit volume, ##g## is Lande factor, ##\mu_B## Bohr magneton, ##J## total angular quantum number, ##x## is the ratio of the Zeeman energy of the magnetic moment in the external field to the thermal energy ##k_B T##. ##x=\frac{g\mu_B\mu_0 H}{k_B T}##.
$$B_J(x)=\frac{2J+1}{2J}\coth (\frac{2J+1}{2J}x)-\frac{1}{2J}\coth (\frac{1}{2J}x)$$
If ##J \rightarrow \infty## then ##B_J(x)## becomes ##L(x)=\coth x-\frac{1}{x}##. How when you have ##J## in definition of ##x##?