Formula:5595

Digital Library of Mathematical Functions ID 14.17.E17

${\displaystyle{\displaystyle\int_{0}^{\pi}\mathsf{Q}_{l}\left(\cos\theta\right)\mathsf{P}_{m}\left(\cos\theta\right)\mathsf{P}_{n}\left(\cos\theta\right)\sin\theta\mathrm{d}\theta=0,}}$

Constraint(s)

${\displaystyle{\displaystyle|m-n|<l<m+n}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=\mathsf{P}^{0}_{\nu}\left(x\right)}}$:
• ${\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=\mathsf{Q}^{0}_{\nu}\left(x\right)}}$:
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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