Formula:5479

Digital Library of Mathematical Functions ID 14.8.E8

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

Constraint(s)

${\displaystyle{\displaystyle\nu\pm m\neq-1,-2,-3,\dots}}$

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
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle\nu}}$: general degree
 

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