$$ Y_{lm}(\theta,\ \phi) =(i)^{m+|m|} \sqrt{{(2l+1)\over 4\pi}{(l - |m|)!\over (l+|m|)!}} \, P_{lm} (\cos{\theta}) \, e^{im\phi} $$
$$ R_{nl} (r) = \sqrt {{\left ( \frac{2 }{n a_{\mu}} \right ) }^3\frac{(n-l-1)!}{2n[(n+l)!]^3} } e^{- r / {n a_{\mu}}} \left ( \frac{2 r}{n a_{\mu}} \right )^{l} L_{n-l-1}^{2l+1} \left ( \frac{2 r}{n a_{\mu}} \right ) $$
$$ R_{nl} (r) = \sqrt {{\left ( \frac{2 }{n a_{\mu}} \right ) }^3\frac{(n-l-1)!}{2n[(n+l)!]^3} } e^{- r / {n a_{\mu}}} \left ( \frac{2 r}{n a_{\mu}} \right )^{l} L_{n-l-1}^{2l+1} \left ( \frac{2 r}{n a_{\mu}} \right ) $$
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