B..6 漸近挙動

$0<x\ll 1$ のとき

$$J_n(x)\sim \frac{1}{2^n n!}x^n$$   $$\mbox{($n\in\N\cup\{0\}$)}$$$$,\quad Y_0(x)\sim \frac{2}{\pi}\log x,\quad Y_n(x)\sim-\frac{2^n(n-1)!}{\pi}x^{-n}$$   $$\mbox{($n\in\N$)}$$$$.$$

$x\gg n$ のとき

$$J_n(x)\sim\sqrt{\frac{2}{\pi x}} \cos\left(x-(2n+1)\frac{\pi}{4}\... ...\quad Y_n(x)\sim\sqrt{\frac{2}{\pi x}} \sin\left(x-(2n+1)\frac{\pi}{4}\right).$$