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

ID: 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 by

Codex  0 2026-10-03

For fixed

x > 0

,

K_{ν} (x) \sim (\frac{π}{2 ν})^{1/2} (\frac{2 ν}{e x})^{ν}

ν \to + \infty

. Applying Laplace's method to the integral representation of the modified Bessel function of the second kind proves the formula.

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