Formula:5668

Digital Library of Mathematical Functions ID 14.30.E9

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \FerrersP[]{l}@{\cos@@{\theta_{1}}\cos@@{\theta_{2}}+\sin@@{\theta_{1}}\sin@@{\theta_{2}}\cos@{\phi_{1}-\phi_{2}}}=\frac{4\pi}{2l+1}\sum_{m=-l}^{l}\conj{\sphharmonicY{l}{m}@{\theta_{1}}{\phi_{1}}}\sphharmonicY{l}{m}@{\theta_{2}}{\phi_{2}}.}

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\overline{\NVar{z}}}}$: complex conjugate
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=\mathsf{P}^{0}_{\nu}\left(x\right)}}$:
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle Y_{{\NVar{l}},{\NVar{m}}}\left(\NVar{\theta},\NVar{\phi}\right)}}$: spherical harmonic
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle l}}$: nonnegative integer
 

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