Formula:5545

Digital Library of Mathematical Functions ID 14.15.E2

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

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: associated Legendre function of the first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\mu}}$: general order
• ${\displaystyle{\displaystyle\nu}}$: general degree
• ${\displaystyle{\displaystyle u}}$: u
 

Resources that cite this formula

No records found.