Formula:5599

Digital Library of Mathematical Functions ID 14.18.E1

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \FerrersP[]{\nu}@{\cos@@{\theta_{1}}\cos@@{\theta_{2}}+\sin@@{\theta_{1}}\sin@@{\theta_{2}}\cos@@{\phi}}=\FerrersP[]{\nu}@{\cos@@{\theta_{1}}}\FerrersP[]{\nu}@{\cos@@{\theta_{2}}}+2\sum_{m=1}^{\infty}(-1)^{m}\FerrersP[-m]{\nu}@{\cos@@{\theta_{1}}}\FerrersP[m]{\nu}@{\cos@@{\theta_{2}}}\cos@{m\phi},}

Symbols List

• ${\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Ferrers function of the first kind
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: 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
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle\nu}}$: general degree
• ${\displaystyle{\displaystyle\theta_{1}}}$: real
• ${\displaystyle{\displaystyle\phi}}$: real
 

Resources that cite this formula

No records found.