Formula:5603

Digital Library of Mathematical Functions ID 14.18.E5

${\displaystyle{\displaystyle Q_{\nu}\left(\cosh\xi_{1}\cosh\xi_{2}-\sinh\xi_{1}\sinh\xi_{2}\cos\phi\right)=P_{\nu}\left(\cosh\xi_{1}\right)Q_{\nu}\left(\cosh\xi_{2}\right)+2\sum_{m=1}^{\infty}(-1)^{m}P^{-m}_{\nu}\left(\cosh\xi_{1}\right)Q^{m}_{\nu}\left(\cosh\xi_{2}\right)\cos\left(m\phi\right).}}$

Symbols List

• ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: associated Legendre function of the first kind
• ${\displaystyle{\displaystyle Q^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}\left(z\right)}}$:
• ${\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}\left(z\right)}}$:
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle\nu}}$: general degree
• ${\displaystyle{\displaystyle\phi}}$: real
• ${\displaystyle{\displaystyle\xi_{1}}}$: positive
 

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