🚀 go-pugleaf

$B>>K\!w?t3X2J$/$:$l$G$9!#(B

$B#29`78?t(BC(n,x)$B$r(Bx$B$K$D$$$FO"B3$H9M(B$B$($?>l9g$K$D$$$F!#(B
$BED>B;a$N9M;!$+$i!"99$KF'$_9~$s$G$_$^$7$?!#(B

 n$B$,@0?t$J$i$P(B

C(n,x)$B!a&#(B(n+1)/$B&#(B(x+1)$B&#(B(n+1-x)
       $B!a&#(B(n+1)/x(1-x)...(n-x)$B&#(B(x)$B&#(B(1-x)
       $B!a&#(B(n+1)sin$B&P(Bx/$B&P(Bx(1-x)...(n-x)

$B$5$i$K(B
sin$B&P(Bx/$B&P(Bx$B!a(B(1-x^2)(1-(x/2)^2)...	$B!JL58B>h@Q!K(B
(1-x)...(n-x)$B!a(Bn!(1-x)(1-x/2)...(1-x/n)
n!$B!a&#(B(n+1)
$B$+(B$B$i(B

       $B!a(B(1-x^2)(1-(x/2)^2).../(1-x)(1-x/2)...(1-x/n)
       $B!a(B(1-(x/(n+1))^2)...(1+x)....(1+x/n)

$B$H$J$k!#(B

$B$3$l$O(B0,...,n$B$r=|$/Am$F$N@0?t>e$KNmE@$r$b$D@04X?t$G$"$k!#(B
 n$B$,@0?t$G$J$$>l9g$K$D$$$F$OITL@(B$B$G$"$k$,!"(B
$B&#4X?t$NL58B>h@QI=<(Ey$+$i9M$($F(B
$B@5$NB&$NGH$NNmE@$,@0?t$N$H$3$m$+$i$:$l$k$?$a!"(B
x>n$B$N@0?t$N(B$B>l9g$b(B0$B$H$O$J$i$J$$$N$G$O$J$$$+$H9M$($i$l$k!#(B

$B$3$N$^$^$G$O(B n$B$,Bg$-$/$J$k$K$D$l!":GBgE@$,@5$NJ}8~$K0\(B$BF0$9$k$N$G(B
$B:GBgE@$r#0$K8GDj$9$k$3$H$r9M$($k!#(B

$B6v?t(B2n$B$N>l9g!"(BC'(2n,x)$B!a(BC(2n,(x+n))$B$H$9$l$P(B

C'(n,x)$B!a(B((2n)!/n!n!)(1-(x/(n+1))^2)...

$B$H9M$($i$l$k!#(B
$B$3$N>l9g!":GBgE@#0$G$NCM$O(B((2n)!/n!n!)$B$G$"$k!#(B

$B$H$3$m(B$B$G!"(BC(n,0)+...+C(n,n)=2^n$B!!$G$"$k$N$G!"(B
C''(n,x)=C'(n,x)/2^n$B$H$7$F$=$N%0%i%U$rIA$$$F$_$?$H$3$m(B
n$B$,Bg$-(B$B$/$J$k$K$D$l!";3$O$J$@$i$+$K$J$C$F!"(B x$B<4$K@\6a$7$F$$$/$h$&$@!#(B

$B!tEv=i9M$($F$$$?(B Gauss$B$N8m:94X?t(B
$B!t(BC1*exp(C2*(-x^2))	(C1,C2$B$ODj?t(B)
$B!t$H$N4X78$K$D$$$F$O!"0MA3ITL@$G$"$k$,!"(B
$B!t$"$k<o$N6K8BA`:n$K$h$C$F!">e(B$B$N$h$&$J7?$N4X?t$K(B
$B!t<}B+$5$;$k$3$H$O2DG=$+$b$7$l$J$$!#(B