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Hylleraas variational function for ground state of helium
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\begin{eqnarrqy}
s=r_1+r_2 & \ \ \ \   t= r_1-r_2 \ \ \ \ &  u=r_{12}=| \mathbf { r }_1 -  \mathbf { r }_2   | 
 \ \ \nonumber \\
s  \in  (0, \infty)   & \ \ \ \  t \in ( -\infty,  \infty ) &
u  \in  (0, \infty)    \nonumber
\end{eqnarrqy}
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$$
\psi(s,t,u)= e^{-ks} \sum_{l,m,n=0}^N  c_{l,2 m,n} \ s^l \ \ t^{2m}\ \  u^n
$$
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