数学物理方程教案3-3anew

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1、§3.3.1&2V4õªÄ5!õªL«–TypesetbyFoilTEX–Page1§3.3.1&2V4õªÄ5!õªL«1dn(x2−1)n.Pn(x)=2n·n!dxnRodriguesúª–TypesetbyFoilTEX–Page1§3.3.1&2V4õªÄ5!õªL«1dn(x2−1)n.Pn(x)=2n·n!dxnRodriguesúªn[]P2(−1)k(2n−2k)!P(x)=xn−2kn2n·k!(n−k)!(n−2k)!k=0Ù¥(–TypesetbyFoilTEX–Page1§3.3.1&2V4õªÄ

2、5!õªL«1dn(x2−1)n.Pn(x)=2n·n!dxnRodriguesúªn[]P2(−1)k(2n−2k)!P(x)=xn−2kn2n·k!(n−k)!(n−2k)!k=0Ù¥hi(n=2–TypesetbyFoilTEX–Page1§3.3.1&2V4õªÄ5!õªL«1dn(x2−1)n.Pn(x)=2n·n!dxnRodriguesúªn[]P2(−1)k(2n−2k)!P(x)=xn−2kn2n·k!(n−k)!(n−2k)!k=0Ù¥h(innnóê2=2–TypesetbyFoilTEX–Page1§3.3.1&2V

3、4õªÄ5!õªL«1dn(x2−1)n.Pn(x)=2n·n!dxnRodriguesúªn[]P2(−1)k(2n−2k)!P(x)=xn−2kn2n·k!(n−k)!(n−2k)!k=0Ù¥h(innnóê2=n−12nÛê2–TypesetbyFoilTEX–Page1y²:

4、^ªúª,k2n(x−1)=–TypesetbyFoilTEX–Page2y²:

5、^ªúª,kXn(−1)kn!2n2n−2k(x−1)=xk!(n−k)!k=0–TypesetbyFoilTEX–Page2y²:

6、^ªúª,kXn(−1)kn!2n2n

7、−2k(x−1)=xk!(n−k)!k=0@oéÙ©–TypesetbyFoilTEX–Page2y²:

8、^ªúª,kXn(−1)kn!2n2n−2k(x−1)=xk!(n−k)!k=0@oéÙ©1dn2n(x−1)=?2nn!dxn–TypesetbyFoilTEX–Page2–TypesetbyFoilTEX–Page3nPn(−1)kn!1dx2n−2k2nn!dxnk!(n−k)!k=0–TypesetbyFoilTEX–Page3nPn(−1)kn!1dx2n−2k2nn!dxnk!(n−k)!k=0Pn(−1)kn!n=

9、1d(x2n−2k)2nn!k!(n−k)!dxnk=0–TypesetbyFoilTEX–Page3nPn(−1)kn!1dx2n−2k2nn!dxnk!(n−k)!k=0Pn(−1)kn!n=1d(x2n−2k)2nn!k!(n−k)!dxnk=0n[]P2(−1)kn!1=n(2n−2k)(2n−2k−1)2n!k!(n−k)!k=0–TypesetbyFoilTEX–Page3nPn(−1)kn!1dx2n−2k2nn!dxnk!(n−k)!k=0Pn(−1)kn!n=1d(x2n−2k)2nn!k!(n−k)!dxnk=0n[

10、]P2(−1)kn!1=n(2n−2k)(2n−2k−1)2n!k!(n−k)!k=0
···(2n−(n−1)−2k)xn−2k–TypesetbyFoilTEX–Page3nPn(−1)kn!1dx2n−2k2nn!dxnk!(n−k)!k=0Pn(−1)kn!n=1d(x2n−2k)2nn!k!(n−k)!dxnk=0n[]P2(−1)kn!1=n(2n−2k)(2n−2k−1)2n!k!(n−k)!k=0
···(2n−(n−1)−2k)xn−2kn[]P2(−1)k(2n−2k)!=xn−2k2nk!(n−k)!(n−2k)!k

11、=0–TypesetbyFoilTEX–Page3nPn(−1)kn!1dx2n−2k2nn!dxnk!(n−k)!k=0Pn(−1)kn!n=1d(x2n−2k)2nn!k!(n−k)!dxnk=0n[]P2(−1)kn!1=n(2n−2k)(2n−2k−1)2n!k!(n−k)!k=0
···(2n−(n−1)−2k)xn−2kn[]P2(−1)k(2n−2k)!n−2k=x¦ÚþC´Ïn−k>0±yEõª2nk!(n−k)!(n−2k)!2k=0–TypesetbyFoilTEX–Page3[n]X2k(−1)(2n−2k)!n−2

12、kPn(x)=x2n·k!(n−k)!(n−2k)!k=0–TypesetbyFoilTEX–Page4[n]X2k(−1)(2n−2k