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- #1

\[

Y_{\ell}^m(0,\varphi) = \delta_{m,0}\sqrt{\frac{2\ell + 1}{4\pi}}.

\]

When \(m = 0\), I obtain \(\sqrt{\frac{2\ell + 1}{4\pi}}\).

However, I am not getting 0 for other \(m\). Plus, to show this is true, I can't methodically go through each \(m\).

How can I do this?