第4章3泰勒级数1ppt课件

1、( )f z0,zD 0z0|,zR z( )f z ( )fz d K 12 i 1z 001()zzz 01z 0011zzz 0n 101()nz 0()nzz 0z ( )f ( )f K d K d 0n 2!in ( )0()nfz0( )( )znf 0n !n( )0()nfz0()nzz 0()nzz 1 0zz ( )f z0,zD 0zz ( )f z( )f z0n !n( )0()nfz0()nzz 0( )f z 0( )f z 0()zz 0()fz 20()zz . ( )0()nfz0()nzz . ( )f z( )f zR |R 2!n10zz |ze1

2、212!z 1.!nzn . | | z 414!z ze 1 212!z 414!z ( 1).!nnzn . shz2 zzee z 515!z .(21)!n 21nz . | | z | | z chz2 zzee 1 414!z .(2 )!n 2nz. sinzz 515!z . | | z cosz1 414!z . | | z .(21)!n 21nz ( 1)n .(2 )!n ( 1)n 2nzz 313!z z 313!z 313!z 717!z 212!z 616!z 313!z 717!z 212!z 616!z nznc0n 2coszcosz| | z 2cosz

3、1 814!z .(2 )!n ( 1)n 4nz. R 2ze2sinz| | z ze1 212!z . 2ze1 412!z . sinzz 515!z . 2sinz2z 1015!z . 2ze2sinz2z 4z 613z . R 1 414!z . .(2 )!n ( 1)n 2nz212!z 412!z z 313!z 313!z 2z 613!z 613!z 1 . 11z | | 1z 21(1)z 13z .nz 23z 1.nnz . | | 1z 32(1)z 22.(1)nn nz . 31(1)z 2(1).2nn nz . 1R 11z 1 3z .( 1)nn

4、z . | | 1z z 2z 4z 2z 34z 6z 212z 126z 3z z 2z 4z 3z3z6z9z12z3nz11z ln(1)z z 313z 414z 1( 1).1nnzn . 21(1)z 1 23z 34z 1.( 1)nnnz . 1 . 11z | | 1z 3z .nz z 2z 4z 1 3z .( 1)nnz . z 2z 4z 212z 2z 21(1)z 1 23z 34 z 1.( 1)n . 2z 2z1nn z 2z4z6z22nz 1R | | 1z () 1nz nc0n 1z 0n nw11w | 1w 1 0n (1)nz 12z 0n

5、1(1)nz 1z R 1z 1z 1 22 1z 1z 1z 2 (1)z 12z 12z 12z ( 1)n 2n( 1)n 12n 1 w 12 (1)z ()2nz nc0n 2z 22z 22z 212 112 0n (2)nz 2z 11z 113 13 2z 0n (2)nz 0n (2)nz R z(1)z 311z z(1)z 42z 32z 214z 1213z 4 3 ( 1)n 4n( 1)n 3n( 1)n 212n ( 1)n 13n (2)z (2)z a( )f z( )f z( )f a( )f a ()za ()( )mfa()mza . !m. 1()(

6、)mfa 1()mza (1)!m ( )f a0, ( )fa (1).,( )mfa ()( )mfa0 0, 0, a( )f z( )f z 3()za ,a( )f z mma( )f za( )f zmc0 sinzz 515!z . 313!z z 0zsinz 0, 313!z515!z . 33z2sinz 0,20,3z2sinz( )f zmc ()mza 1mc 1()mza . ()mza mc1mc ()za . ()mza ( ) z a( )f z( )f z()mza ( ) z ( )a a( ) z 0 ( )a mc 0 ( )f z cosz,2 3,

7、2 5,2 .( )fz sin , z ()2f 1 0, 1( )f z 21z i ( )fz 2 , z()fi 2i 1( )f z 21z (3)i 33()zi 3()zi ( )f z 1nz e21kin 10z sinz0z ( )f z ( )f zshz 2z shz.(21)!n 21nz . sinzz 515!z . | | z .(21)!n 21nz ( 1)n 525!z13213!z . ( )f z 929!z 313!z 717!z z 515!z 313!z 717!z sinzshz 2z 525!z 13213!z . 929!z 0z 2ze(

8、 )f z 1 ze1 212!z . z 2z2z4z20z( )f z(1),m 0z( )fz ( )f z0()mzz ( ) z 0z( ) z 0()z ( )fz 10()mm zz ( ) z 0()mzz ( ) z 10()mzz ( )mz 0()zz ( )z ( )h z ( )mz 0()zz ( ) z ( ),z ( ) z 0z( )h z0z0()h z0()mz 10()mzz ( )h z0z( )fz 0, 0, (1)nz nc0n 21z1z 0n nw11w | 1w 1z 1 w 1z 0n (1)nz 21z1n 1(1)nn z R 1 1

9、1 |1z (1)z 1(1)nzi nc0n 14 3z 1zi 14 3z 1 1 3i 11 3i 111 3i 0n (1)nzi 0n (1)nzi 1 (1)zi R 3 1031033(1)1 3zii 31 3i (1)zi 3n(1 3 )ni 3n1(1 3 )ni (1)zi ( )f z 00z 2e d 0z ze0n 2n | | z 2e | 0n ( )f z 2e d 0z 1!n0n (21)n | | z nz1!n21nz 1!n2sin(2)zz 01z cosz0n | | z ( 1)(2 )!nn 2sin(2)zz sin sin1 2cos(1)z cos1 2sin(1)z sinz0n ( 1)(21)!nn 0n ( 1) sin1n 0n |1|z 4(1)nz 42(1)nz 2nz21nz 21 (1) z (2 )!n( 1) cos1n (21)!n 225zz 01z | | 1z 11 z 0n nz225zzz 24 (1)z 24 (1)z 14z 14 0n ( 1)n 0n |1|z z1z 121(1)14z 21(1)14z