Formula:5588

Digital Library of Mathematical Functions ID 14.17.E10

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

Constraint(s)

${\displaystyle{\displaystyle-\nu-1}}$

Symbols List

• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \cpi} : 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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