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Modified Bessel function

Modified Bessel function of the second kind

For fixed $x>0$,
$$
K_\nu(x)\sim\left(\frac\pi{2\nu}\right)^{1/2}
\left(\frac{2\nu}{ex}\right)^\nu
$$
as $\nu\to+\infty$. Applying <Laplace's method> to the <integral representation of the modified Bessel function of the second kind> proves the formula.

Large-order asymptotic of the modified Bessel function of the second kind

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 31B / b / Solution

Large-order asymptotic of the modified Bessel function of the second kind

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Large-order asymptotic of the modified Bessel function of the second kind

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