Corollary A.8.1 . [0578] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Corollary A.8.1 .
Let ν > 0 \nu>0
(A.46) lim y → + ∞ I ν ( y ) e y 2 π y = 1 \lim\limits_{y\to+\infty}\frac{I_{\nu}(y)}{\frac{e^{y}}{\sqrt{2\pi y}}}=1
and
(A.47) lim y → + ∞ K ν ( y ) π 2 y ⋅ e − y = 1 . \lim\limits_{y\to+\infty}\frac{K_{\nu}(y)}{\sqrt{\frac{\pi}{2y}}\cdot e^{-y}}=1.