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I am trying to determine the expansion that requires using $3j$ symbols; however, I am running into some conceptual snags. First, the expansion produces symbols that have m's that do not agree with the quantum number requirement that $m=-l, -l+1,..., l$. I assume I can simply throw these out. Second, I am determining $m=m_1$ by evaluating $m_1+m_2=m_3$. I will never have a nonzero term because $m_1+m_2+m_3=0$. Can someone explain?

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