What is the Integral of the product of spherical harmonics and derivatives of spherical harmonics? More precisely, I am looking for $$\int_\Omega d\Omega\, Y_{l}^m Y_{l^\prime}^{m^\prime} \partial_\theta Y_{l^{\prime\prime}}^{m^{\prime\prime}}$$ and $$\int_\Omega d\Omega\, Y_{l}^m \partial_\theta Y_{l^\prime}^{m^\prime} \partial_\theta Y_{l^{\prime\prime}}^{m^{\prime\prime}}$$
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I know $\int_\Omega d\Omega, Y_{l}^m Y_{l^\prime}^{m^\prime} Y_{l^{\prime\prime}}^{m^{\prime\prime}}$ in discussed here: https://physics.stackexchange.com/questions/10039/integral-of-the-product-of-three-spherical-harmonics – Fluid Feb 27 '18 at 00:02