A..2 Bessel $B$NHyJ,J}Dx<0(B

A..2.3 $B2r$N4pK\7O(B

$\nu\in\C\setminus\Z$ $B$G$"$k$H$-!"(B $J_{\nu}(x)$, $J_{-\nu}(x)$ $B$O(B1$B3) $B$N2r$N4pK\7O$K$J$k(B)$B!#(B $B$3$l$ON> $B$N$H$-$NA}BgEY$r9M$($F$bMF0W$K>ZL@$G$-$k$,!"(B $B

Proof. ($B>JN,(B) $\qedsymbol$ ARRAY(0xe434a4) $\qedsymbol$

$B%m%s%9%-%"%s$NEy<0$+$iA[A|$G$-$k$3$H$@$,!"(B $\nu=n\in\Z$ $B$N$H$-(B $J_\nu(x)$, $J_{-\nu}(x)$ $B$O(B1$BB0$K$J$k!#(B $B$3$l$OMF0W$K3N$+$a$i$l$k4X78(B

$$J_{-n}(z)=(-1)^n J_n(z)$$

$B$+$iL@$i$+$G$"$k!#(B

$B$5$F!"(B $B$$$h$$$hBhFs$B%N%$%^%s4X?t(B$B$H$b$$$&(B) $Y_\nu (x)$ $B$rF3F~$7$h$&!#(B

$B$^$:(B $\nu\in\C\setminus\Z$ $B$N>l9g$K(B

$$Y_\nu(x):= \frac{\cos\nu\pi J_\nu(x)-J_{-\nu}(x)}{\sin\nu\pi}$$

$B$H$*$/!#(B $B$3$l$O(B $J_\nu(x)$, $J_{-\nu}(x)$ $B$N@~7?7k9g$G$"$k$+$i!"(B (3) $B$N2r$G$"$k!#(B $B$^$?JdBj(B A.1 $B$h$jMF0W$K(B

$$W(J_{\nu}(x),Y_{\nu}(x))=\frac{2}{\pi x} \mbox{($\nu\in\C\setminus\Z$)}$$ (5)

$B$,J,$+$k$N$G!"(B$J_\nu(x)$, $Y_\nu (x)$ $B$O(B (3) $B$N2r$N4pK\7O$G$"$k!#(B

$B$5$i$K(B $n\in\Z$ $B$KBP$7$F9-5A0lMM<}B+6K8B(B

$$\lim_{\nu\to n}Y_\nu(x)$$

$B$,B8:_$9$k!#$=$3$G(B

$$Y_n(x):=\lim_{\nu\to n}Y_\nu(x)$$

$B$H$*$/$H!"(B $B$3$l$b(B (3) $B$N2r$G$"$k$,!"(B (5) $B$h$j(B⁷

$$W(J_{n}(x),Y_{n}(x)) =\lim_{\nu\to n} W(J_{\nu}(x),Y_{\nu}(x)) =\frac{2}{\pi x}\ne 0$$

$B$G$"$k$+$i!"(B $J_n(x)$, $Y_n(x)$ $B$O(B ($\nu=n$ $B$N$H$-$N(B) (3) $B$N2r$N4pK\7O$G$"$k!#(B

$B0J>e$r$^$H$a$k$H

A..2 Bessel $B$NHyJ,J}Dx<0(B