Formula:5484

Digital Library of Mathematical Functions ID 14.8.E13

${\displaystyle{\displaystyle P^{\mu}_{\nu}\left(x\right)\sim\frac{\Gamma\left(-\nu-\frac{1}{2}\right)}{\pi^{1/2}\Gamma\left(-\mu-\nu\right)(2x)^{\nu+1}},}}$

Constraint(s)

${\displaystyle{\displaystyle\Re\nu<-\tfrac{1}{2}}}$
${\displaystyle{\displaystyle\Re\nu<-\tfrac{1}{2}}}$
${\displaystyle{\displaystyle\nu+\mu\neq 0,1,2,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: associated Legendre function of the first kind
• ${\displaystyle{\displaystyle\sim}}$: asymptotic equality
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\mu}}$: general order
• ${\displaystyle{\displaystyle\nu}}$: general degree
 

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