自考第4章2幂级数ppt课件

1、( )nfz1( ),fz2( ),fz .,(.),nfz1( )fz2( )fz .( )nfz ( )nfz1n ( )nSz 1( )fz2( )fz . 0()nSzn 0()S z0()nSzlimn 0()S z 0z0z0z0z( )nfz1n 0()S z( )S z1( )fz 2( )fz . ( )S z( )S z( )nfz()nncza ( )nfznnc z .( )nfz . 0n 0n ()nncza 0c 1()c za 22()c za .()nnc za nnc z0c 1c z 22c z .nnc z 00z 0nnc z0n 0z0z0z0zO0

2、|z0zzz0n nnc z0nnc z0n z0n nnc z0n ()nncza a0zzza 0n ()nncza . . 0za 0n nnc z0z 0z | | | | | | |0n (1)nncz 11 z0n (1)nncz 220z30n (2)nncz 1z 11 | |ORz0n nna z0n nna z0n nna zzz0n nna zzR | |zR | |zR | |zR | |ORz0n nna z0z0nna z0n nna z0 0nna znna z0n 0n nna z0n nna zz0z | | |0n nc0n nc0n nnc zO1zz0n

3、 nc0n nnc z0n nnc z0n 0nnc z0z0n nnc z0n |nc|z1 | |0z1 | |z0z | | |0n nnc z0n nnc z0n z1 | |nc |0n nana1na limn l 0, R nanlimn l 0, R 1l1lnz1n napnnz1pn 1nnaa limn limn 1 R 1n nn2( !)nnzna nn2( !)n1nnaa 1(1)nn (1)!n nn!n nn(1)nn (1)n (1)n 1(1)nn limn limn limn limn R 10(1)!n !n pn(1)pn nn(1)ni 0n na

4、 (1)ni nzlimn 2()nn2 limn limn R 22 1n ine nzna ine cossininn 1 na1 nlimn R 1210n nna z0a 1a z 22a z .nna z . ( )f z( )f z1| | zR 0n nnb z0b 1bz 22b z .nnb z . ( )g z( )g z2| | zR | | z 12,R R()nnab nz0n 0n nna z0n nnb z ( )f z( )g z0(a 1a z 22a z .nna z ). 0(b1bz 22b z .nnb z ). 0a 0b ()z 0 1a b1 0

5、a b 2()z 0 2a b1 1a b 2 0a b . ()nz 0 na b11na b 1 1.nab 0na b . min0n nna z0n nnb z()nnab nz0n 0.110.1nn nz0n 1nncc 0.110.1nn 110.110.1nn limn limn 0.1 101 0n nz110.1n nz0n 0.110.1nn 1(1)10.1n nznz0n 0n 0n nz110.1n nz0n O1z10z1 | |limn 1nnaa 0n na,nz1nan nna,nznz0n 0n limn 1nnaa 1nnaa limn l 111nna

6、 1nan 1nnaa limn limn l 12nn 1nnaa limn nna1()1nna limn limn 1nnaa 1nn l 1nnaa limn R 1ldzaz 0n ()nnaza 0a 1()a za 22()a za ( )f z( )f z|zaR .()nnaza . ( )f z|zaR ( )f z( )f z 1a 22 ()a za 1.()nnnaza . |zaR 1n nna( )f z( )f z0()aza 211()2a za 11.()1nnazan . 0n 11nan 1()nza 1()nza |zaR 0n nna z0a 1a

7、z 22a z .nna z . ( )f z( )f z| | zwwwwwf( )g z0a 1a 22a .nna |. ( )g z( )g z( )g z( )g z0n nz1 z 2z 3z .nz . ( )nsz 211.nzzz 1z | | 1z 1nz nzlimn 0 ( )nszlimn 11z 11z | | zwww www11z 1 . | | zw| | 2z 12z 12 112z 12 | 12z 0n 0n 1( 1)2nnnz ()2nz R R 1 1 z 2z .( 1)nnz 0n nz21.nzzz . 11z | | 1z www www1bz 0n nc0()