三、重根 设F(S)在s1处有三重根，则： F(S)= N(S) N(S) K13 K12 K K2 D(S)(S-S)3(S-S2)(S-S)3'(S-S)2'(S-S)S-S2 K:=-s D(S)I5=s 店K+K26-S)+K6-SP+3、6-S门 S-S2 d =K2+2(S-S)K1+ D(S))s=s Ss-s-2+w-高 D(S)
13 12 11 2 3 3 2 1 2 1 1 1 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) N S N S K K K K F S D S S S S S S S S S S S S S = = = + + + − − − − − − 1 3 13 1 ( ) ( ) ( ) S S N S K S S D S = − = 1 2 3 2 13 12 1 11 1 1 2 3 3 2 12 1 11 1 12 1 2 [ ( ) ( ) ( ) ] ( ) 2( ) [( ) ] [( ) ] ( ) S S d K K K S S K S S S S dS S S d d N S K K S S K S S K S S dS S S dS D S = + − + − + − − = + − + − = − − 2 2 3 3 2 2 2 1 11 1 2 ( ) [( ) ] 2 [( ) ] ( ) d N S d K S S K S S dS dS D S S S − = + − − 设F(S)在s1处有三重根，则： 三、重根
-1d2 K 2i(S-5)N(S) D(S) S=S 。，j=0,12L(p-.01=1,4 pp+…+Kpl+Kk0+K,e++Ke =p
1 0 1( ) 1 0 1 ( ) [( ) ] , 0,1,2 ( 1) , 0! 1, 1 ! ( ) j p p j j S S d N S d K S S j p j D S dS dS − = = − = − = = L 1 2 1 1 1( 1) 1 1 1 1 1 12 11 2 ( ) ( ) ( ) [ ] ( 1)! n p p n p p n p p S t S t S t n K K K f t L S S S S S S K t K t K e K e K e p − − − − = + + + − − − = + + + + + + − 1 2 3 11 1 2 1 ( ) [( ) ] 2! ( ) S S d N S K S S dS D S = = −