According to wikipedia, the product of two spherical harmonics is
What I do not understand is the scope of the sum. From where to where does it go, over all integers for L and M?
Also since $m1 + m2 + M$ has to be zero for the Wigner symbols to be non-zero, couldn't we simply insert $M = -m1 - m2$ into the sum?
In my case $|m_1| \leq l_1$ and $|m_2| \leq L_2$ with all being integers.