Formula:5485

Digital Library of Mathematical Functions ID 14.8.E14

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

Constraint(s)

${\displaystyle{\displaystyle\mu\neq\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2},\dots}}$

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
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\mu}}$: general order
 

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