# Proving a dependence between variables

1. Jul 29, 2014

### MathsNewb

1. The problem statement, all variables and given/known data

I want to find the relationship between $\psi$ and $\gamma$ from this equation
$$\Lambda=\sqrt{\gamma ^2+4 \pi ^2 \psi ^2} \sum _{j=0}^{\infty } \frac{\left(\frac{(2 j-1)\text{!!} (2 \pi \psi )^j}{(2 j)\text{!!} \left(\gamma ^2+4 \pi ^2 \psi ^2\right)^{j/2}}\right)^2}{1-2 j}$$ thereby proving a dependence between $\psi$ and $\gamma$ (where $\psi$,$\gamma$ and $\Lambda$ are variables)

2. Relevant equations

The above derives from $$\Lambda=\frac{2 \sqrt{\gamma ^2+4 \pi ^2 \psi ^2} E\left(\frac{4 \psi ^2 \pi ^2}{\gamma ^2+4 \pi ^2 \psi ^2}\right)}{\pi }$$

3. The attempt at a solution

Trying to find a closed form approximation.

Last edited: Jul 29, 2014