Formula:5561

Digital Library of Mathematical Functions ID 14.15.E18

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \assLegendreOlverQ[\mu]{\nu}@{x}=\frac{1}{\beta\EulerGamma@{\nu+\mu+1}}\left(\frac{\alpha^{2}-y}{x^{2}-1+\alpha^{2}}\right)^{1/4}\*\modBesselK{\mu}@{\left(\nu+\tfrac{1}{2}\right)|y|^{1/2}}\left(1+\bigO@{\frac{1}{\nu}}\right),}

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\mu}}$: general order
• ${\displaystyle{\displaystyle\nu}}$: general degree
• ${\displaystyle{\displaystyle\beta}}$: β
• ${\displaystyle{\displaystyle y}}$: y
• ${\displaystyle{\displaystyle\alpha}}$: α
 

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