Hyperbolic Debye asymptotic for Legendre polynomials (source code)

= Hyperbolic Debye asymptotic for Legendre polynomials
{c}

For fixed $\xi>0$,
$$
P_n(\cosh\xi)
\sim
\frac{e^{(n+1/2)\xi}}{\sqrt{2\pi n\sinh\xi}}.
$$