Formula:5560

Digital Library of Mathematical Functions ID 14.15.E17

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \assLegendreP[-\mu]{\nu}@{x}=\beta\left(\frac{\alpha^{2}-y}{x^{2}-1+\alpha^{2}}\right)^{1/4}\modBesselI{\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
• ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: associated Legendre function of the first kind
• ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the first 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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