Formula:5589

Digital Library of Mathematical Functions ID 14.17.E11

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \int_{-1}^{1}\left(\FerrersP[]{\nu}@{x}\right)^{2}\diff{x}=\frac{\pi^{2}-2\sin^{2}@{\nu\pi}\digamma'@{\nu+1}}{\pi^{2}\left(\nu+\frac{1}{2}\right)},}

Constraint(s)

${\displaystyle{\displaystyle\nu\neq-\frac{1}{2}}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=\mathsf{P}^{0}_{\nu}\left(x\right)}}$:
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: general degree
 

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