deletions | additions       diff --git a/where_beta_tilde_i_2__.tex b/where_beta_tilde_i_2__.tex  index c8e0ebb..0a54a1e 100644  --- a/where_beta_tilde_i_2__.tex  +++ b/where_beta_tilde_i_2__.tex 
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where $\beta={{<{\tilde i}^{2}>}^{1/2}} / {{<{\tilde e}^{2}>}^{1/2}}$, $K_\lambda=K([3(1-\lambda^2)]^{1/2}/2)$ and $E_\lambda=E([3(1-\lambda^2)]^{1/2}/2)$, with $K(x)$ and $E(x)$ being the Complete Elliptic Integrals of the first and second kind respectively.  The CEIs are able to be expressed as power series, where $K(x)=\frac{\pi}{2}\sum_{n=0}^{\infty}[\frac{(2n)!}{2^{2n}(n!)^2}]^2x^{2n}$ and $E(x)=\frac{\pi}{2}\sum_{n=0}^{\infty}[\frac{(2n)!}{2^{2n}(n!)^2}]^2\frac{x^{2n}}{1-2n}$ Being an infinite sum, the CEIs are approximated up to $n=20$ with $x=[3(1-\lambda^2)]^{1/2}/2$. Since the intergals of Eqn 10 go from $0<=\lambda<=1$