Formula:5406

Digital Library of Mathematical Functions ID 14.3.E20

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \frac{2\sin@{\mu\pi}}{\pi}\assLegendreOlverQ[\mu]{\nu}@{x}=\frac{(x+1)^{\mu/2}}{\EulerGamma@{\nu+\mu+1}(x-1)^{\mu/2}}\hyperOlverF@{\nu+1}{-\nu}{1-\mu}{\tfrac{1}{2}-\tfrac{1}{2}x}-\frac{(x-1)^{\mu/2}}{\EulerGamma@{\nu-\mu+1}(x+1)^{\mu/2}}\hyperOlverF@{\nu+1}{-\nu}{\mu+1}{\tfrac{1}{2}-\tfrac{1}{2}x}.}

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: Olver’s hypergeometric function
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\mu}}$: general order
• ${\displaystyle{\displaystyle\nu}}$: general degree
 

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