Formula:5581

Digital Library of Mathematical Functions ID 14.17.E3

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

Constraint(s)

${\displaystyle{\displaystyle\nu\neq 0,-1}}$

Symbols List

• ${\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Ferrers function of the first kind
• ${\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Ferrers function of the second kind
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \diff{\NVar{x}}} : differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\mu}}$: general order
• ${\displaystyle{\displaystyle\nu}}$: general degree
 

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