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Proving a dependence between variables

  1. Jul 29, 2014 #1
    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
  2. jcsd
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