{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 598 "with(combinat, choo se);\nA(0) := 1/y;y:=f(x);\nB(0) := diff(y,x)/y;\nfor i from 1 to 5 do w := i;\nA(w) := simplify(sum('(-1)^(a-1)*y^(a-1)*diff(y,x$w)*y^(w-a+ 1)*A(w-a)/a!','a'=1..w)/y^(w+1));\nB(w) := simplify(sum('(-1)^(a)*y^(a )*diff(y,x$(w+1))*y^(w-a+1)*A(w-a)/a!','a'=1..w)/y^(w+1)); l:=0;\nAL(0 ,0):=A(0); BL(0,0) := B(0); AL(l,w) := simplify(sum('(-1)^(a)*a!*x^(l- a)*y^a*y^(w-a+1)*A(w-a)','a'=1..max(w,w))/y^(w+1));\nBL(l,w) := simpli fy(sum('(-1)^(a)*a!*x^(l-a)*y^a*y^(w-a+1)*B(w-a)','a'=1..max(w,w))/y^( w+1));\nxprime := simplify(x -AL(l,w-1)/AL(l,w));\nxxprime := simplify (x - BL(l,w-1)/BL(l,w));\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#%'c hooseG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6#\"\"!*$-%\"fG6#%\"x G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG-%\"fG6#%\"xG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6#\"\"!*&-%%diffG6$-%\"fG6#%\"x GF/\"\"\"F,!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6#\"\"\"*&-%%diffG6$-%\"fG6#%\" xGF/F'F,!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6#\"\"\",$*&-%% diffG6$-F+6$-%\"fG6#%\"xGF2F2F'F/!\"\"F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$\"\"!F'* $-%\"fG6#%\"xG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#BLG6$\"\"!F '*&-%%diffG6$-%\"fG6#%\"xGF/\"\"\"F,!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$\"\"!\"\"\",$*&%\"xG!\"\"-%\"fG6#F+F,F," }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#BLG6$\"\"!\"\"\",$*(%\"xG!\"\"-%\" fG6#F+F,-%%diffG6$F-F+F(F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xprim eG,$%\"xG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xxprimeG,$%\"xG\" \"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>-%\"AG6#\"\"#,$*(-%%diffG6$-F+6$-%\"fG6#%\"xGF2F2\" \"\",&F-!\"#F/F3F3F/!\"$#!\"\"F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>- %\"BG6#\"\"#,$*(-%\"fG6#%\"xG!\"#-%%diffG6$-F06$-F06$F*F-F-F-\"\"\",&F 4F.F*F6F6#F6F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$\"\"!F'*$-%\"fG6#%\"xG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#BLG6$\"\"!F'*&-%%diffG6$-%\"fG6# %\"xGF/\"\"\"F,!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$\"\"! \"\"#,$*(-%\"fG6#%\"xG!\"#,&*&F.\"\"\"-%%diffG6$F+F.F2F2F+F/F2F.F/!\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#BLG6$\"\"!\"\"#*(-%\"fG6#%\" xG!\"\",&*&-%%diffG6$-F26$F*F-F-\"\"\"F-F6F6F4F(F6F-!\"#" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%'xprimeG*(%\"xG\"\"\",&*&F&F'-%%diffG6$-%\"fG6 #F&F&F'F'F-!\"$F',&F)F'F-!\"#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%(xxprimeG*(%\"xG\"\"\",&*&-%%diffG6$-F+6$-%\"fG6#F&F&F&F'F&F'F'F-\" \"$F',&F)F'F-\"\"#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"$ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6#\"\"$,$*(-%%diffG6$-F+6$- F+6$-%\"fG6#%\"xGF4F4F4\"\"\",**&F-F5F/F5\"\"'*&F1F5F-F5!\"$*&F1F5F/F5 F:*$F1\"\"#F5F5F1!\"%#F5F8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6 #\"\"$,$*(-%\"fG6#%\"xG!\"$-%%diffG6$-F06$-F06$-F06$F*F-F-F-F-\"\"\",* *&F4F8F6F8\"\"'*&F*F8F4F8F.*&F*F8F6F8F.*$F*\"\"#F8F8#!\"\"F;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$\"\"!F'*$-%\"fG6#%\"xG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#BLG6$\"\"!F'*&-%%diffG6$-%\"fG6#%\"xGF/\"\"\"F,!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$\"\"!\"\"$,$*(-%\"fG6#%\"xG! \"$,**(-%%diffG6$-F36$F+F.F.\"\"\"F.\"\"#F5F7!\"#*(F2F7F.F8F+F7F7*(F+F 7F5F7F.F7\"\"%*$F+F8!#7F7F.F/#F7F8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >-%#BLG6$\"\"!\"\"$,$*(-%\"fG6#%\"xG!\"#,**(-%%diffG6$-F36$-F36$F+F.F. F.\"\"\"F.\"\"#F7F9F:*(F2F9F.F:F+F9!\"\"*(F+F9F5F9F.F9!\"%*&F+F9F7F9!# 7F9F.!\"$#F9F:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xprimeG*(%\"xG\" \"\",**(-%%diffG6$-F+6$-%\"fG6#F&F&F&F'F&\"\"#F-F'F2*(F*F'F&F2F/F'!\" \"*(F/F'F-F'F&F'!\"'*$F/F2\"#;F',*F)F2F3F4F5!\"%F7\"#7F4" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%(xxprimeG*(%\"xG\"\"\",**(-%%diffG6$-F+6$-F+6$ -%\"fG6#F&F&F&F&F'F&\"\"#F/F'F4*(F*F'F&F4F1F'!\"\"*(F1F'F-F'F&F'!\"'*& F1F'F/F'!#;F',*F)F4F5F6F7!\"%F9!#7F6" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"wG\"\"%" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"AG6#\"\"%,$*(-%% diffG6$-F+6$-F+6$-F+6$-%\"fG6#%\"xGF6F6F6F6\"\"\",2*(F-F7F/F7F1F7!#C*( F-F7F/F7F3F7\"#7*(F-F7F3F7F1F7F<*&F3\"\"#F-F7!\"%*(F/F7F3F7F1F7F<*&F/F 7F3F?!\"'*&F3F?F1F7F@*$F3\"\"$F7F7F3!\"&#!\"\"\"#C" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>-%\"BG6#\"\"%,$*(-%\"fG6#%\"xG!\"%-%%diffG6$-F06$-F0 6$-F06$-F06$F*F-F-F-F-F-\"\"\",2*(F4F:F6F:F8F:!#C*(F4F:F6F:F*F:\"#7*(F 4F:F*F:F8F:F?*&F*\"\"#F4F:F.*(F6F:F*F:F8F:F?*&F6F:F*FB!\"'*&F*FBF8F:F. *$F*\"\"$F:F:#F:\"#C" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG\"\"!" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$\"\"!F'*$-%\"fG6#%\"xG!\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#BLG6$\"\"!F'*&-%%diffG6$-%\"fG 6#%\"xGF/\"\"\"F,!\"\"" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$\" \"!\"\"%,$*(-%\"fG6#%\"xG!\"%,2**-%%diffG6$-F36$-F36$F+F.F.F.\"\"\"F. \"\"$F5F9F7F9\"\"'**F2F9F.F:F5F9F+F9!\"$**F2F9F.F:F+F9F7F9F=*(F2F9F.F: F+\"\"#F9**F+F9F5F9F.F@F7F9!#7*(F+F@F5F9F.F@F;*(F+F@F7F9F.F9\"#O*$F+F: !$W\"F9F.F/#!\"\"F;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%#BLG6$\"\"! \"\"%,$*(-%\"fG6#%\"xG!\"$,2**-%%diffG6$-F36$-F36$-F36$F+F.F.F.F.\"\" \"F.\"\"$F7F;F9F;\"\"'**F2F;F.F%'xprime G*(%\"xG\"\"\",2**-%%diffG6$-F+6$-F+6$-%\"fG6#F&F&F&F&F'F&\"\"$F-F'F/F '\"\"'**F*F'F&F4F-F'F1F'!\"$**F*F'F&F4F1F'F/F'F7*(F*F'F&F4F1\"\"#F'**F 1F'F-F'F&F:F/F'!#=*(F1F:F-F'F&F:\"\"**(F1F:F/F'F&F'\"#[*$F1F4!$!=F',2F )F5F6F7F8F7F9F'F;!#7F=F5F?\"#OFA!$W\"!\"\"" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(xxprimeG*(%\"xG\"\"\",2**-%%diffG6$-F+6$-F+6$-F+6$-% \"fG6#F&F&F&F&F&F'F&\"\"$F/F'F1F'\"\"'**F*F'F&F6F/F'F3F'!\"$**F*F'F&F6 F3F'F1F'F9*(F*F'F&F6F3\"\"#F'**F3F'F-F'F&F%\"wG\"\"&" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"AG6#\"\"&,$*(-%%diffG6$-F+6$-F+6$-F+6$- F+6$-%\"fG6#%\"xGF8F8F8F8F8\"\"\",B**F-F9F/F9F1F9F3F9!$?\"**F-F9F/F9F1 F9F5F9\"#g**F-F9F/F9F5F9F3F9F>*(F-F9F/F9F5\"\"#!#?**F-F9F1F9F5F9F3F9F> *(F-F9F1F9F5FA!#I*(F-F9F5FAF3F9FB*&F-F9F5\"\"$F'**F/F9F5F9F1F9F3F9F>*( F/F9F5FAF1F9FE*(F/F9F5FAF3F9FE*&F/F9F5FH\"#5*(F1F9F5FAF3F9FB*&F1F9F5FH FM*&F5FHF3F9F'*$F5\"\"%!\"\"F9F5!\"'#FS\"$?\"" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"BG6#\"\"&,$*(-%\"fG6#%\"xG!\"&-%%diffG6$-F06$-F06$ -F06$-F06$-F06$F*F-F-F-F-F-F-\"\"\",B**F4F%\"lG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6 $\"\"!F'*$-%\"fG6#%\"xG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#BL G6$\"\"!F'*&-%%diffG6$-%\"fG6#%\"xGF/\"\"\"F,!\"\"" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>-%#ALG6$\"\"!\"\"&,$*(-%\"fG6#%\"xG!\"&,B*,-%%diffG6 $-F36$-F36$-F36$F+F.F.F.F.\"\"\"F.\"\"%F5F;F7F;F9F;\"#C*,F2F;F.F-% #BLG6$\"\"!\"\"&,$*(-%\"fG6#%\"xG!\"%,B*,-%%diffG6$-F36$-F36$-F36$-F36 $F+F.F.F.F.F.\"\"\"F.\"\"%F7F=F9F=F;F=\"#C*,F2F=F.F>F7F=F9F=F+F=!#7*,F 2F=F.F>F7F=F+F=F;F=FA**F2F=F.F>F+\"\"#F7F=F>*,F2F=F.F>F9F=F+F=F;F=FA** F2F=F.F>F9F=F+FD\"\"'**F2F=F.F>F+FDF;F=F>*(F2F=F.F>F+\"\"$!\"\"*,F+F=F 5F=F.FJF9F=F;F=!#[**F+FDF5F=F.FJF9F=F?**F+FDF5F=F.FJF;F=F?*(F+FJF5F=F. FJ!\")**F+FDF7F=F.FDF;F=\"$W\"*(F+FJF7F=F.FD!#s*(F+FJF9F=F.F=!$w&*&F+F JF;F=!%!)GF=F.!\"&#F=F?" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'xprimeG* (%\"xG\"\"\",B*,-%%diffG6$-F+6$-F+6$-F+6$-%\"fG6#F&F&F&F&F&F'F&\"\"%F- F'F/F'F1F'\"#C*,F*F'F&F6F-F'F/F'F3F'!#7*,F*F'F&F6F-F'F3F'F1F'F9**F*F'F &F6F3\"\"#F-F'F6*,F*F'F&F6F/F'F3F'F1F'F9**F*F'F&F6F/F'F3F<\"\"'**F*F'F &F6F3F*(F3FBF/F'F&FF?F@F6FAFCFD!#[FFF7FHF7FI!\")FJ\"$W\"FLFEFN!$w&FP\"%!)GFC" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%(xxprimeG*(%\"xG\"\"\",B*,-%%diffG6$ -F+6$-F+6$-F+6$-F+6$-%\"fG6#F&F&F&F&F&F&F'F&\"\"%F/F'F1F'F3F'\"#C*,F*F 'F&F8F/F'F1F'F5F'!#7*,F*F'F&F8F/F'F5F'F3F'F;**F*F'F&F8F5\"\"#F/F'F8*,F *F'F&F8F1F'F5F'F3F'F;**F*F'F&F8F1F'F5F>\"\"'**F*F'F&F8F5F>F3F'F8*(F*F' F&F8F5\"\"$!\"\"*,F5F'F-F'F&FDF1F'F3F'!#s**F5F>F-F'F&FDF1F'\"#O**F5F>F -F'F&FDF3F'FI*(F5FDF-F'F&FDF;**F5F>F/F'F&F>F3F'\"$#>*(F5FDF/F'F&F>!#'* *(F5FDF1F'F&F'!$?(*&F5FDF3F'!%cMF',BF)F9F:F;F " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 550 }{VIEWOPTS 1 1 0 1 1 1803 }