Formula:654

Digital Library of Mathematical Functions ID 1.17.E25

${\displaystyle{\displaystyle\delta\left(\cos\theta_{1}-\cos\theta_{2}\right)\delta\left(\phi_{1}-\phi_{2}\right)=\sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{\ell}Y_{{\ell},{m}}\left(\theta_{1},\phi_{1}\right)\overline{Y_{{\ell},{m}}\left(\theta_{2},\phi_{2}\right)}.}}$

Symbols List

• ${\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}$:
• ${\displaystyle{\displaystyle\overline{\NVar{z}}}}$: complex conjugate
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle Y_{{\NVar{l}},{\NVar{m}}}\left(\NVar{\theta},\NVar{\phi}\right)}}$: spherical harmonic
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
 

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