Debye asymptotic for Legendre polynomials
= Debye asymptotic for Legendre polynomials
{c}
For fixed $0<\theta<\pi$,
$$
P_n(\cos\theta)
\sim
\sqrt{\frac{2}{\pi n\sin\theta}}
\cos\left(\left(n+\frac12\right)\theta-\frac\pi4\right).
$$
= Debye asymptotic for Legendre polynomials
{c}
For fixed $0<\theta<\pi$,
$$
P_n(\cos\theta)
\sim
\sqrt{\frac{2}{\pi n\sin\theta}}
\cos\left(\left(n+\frac12\right)\theta-\frac\pi4\right).
$$