Formula:5598

Digital Library of Mathematical Functions ID 14.17.E20

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

Constraint(s)

${\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}\left(z\right)}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: general degree
 

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