Formula:6326

Digital Library of Mathematical Functions ID 18.10.E5

${\displaystyle{\displaystyle P_{n}\left(\cos\theta\right)=\frac{1}{\pi}\int_{0}^{\pi}(\cos\theta+i\sin\theta\cos\phi)^{n}\mathrm{d}\phi.}}$

Symbols List

• ${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}$: Legendre polynomial
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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