{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "Text" -1 200 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 2 0 2 0 2 2 0 1 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "01." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 30 "Delta:=(f,k)->subs(k=k+1,f)-f:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Delta(k^3,k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$),&%\"kG \"\"\"F(F(\"\"$F(F(*$)F'F)F(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "expand(Delta(k^3, k));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"$\"\"\")%\"kG\"\"#F&F& *&F%F&F(F&F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "04." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "fallFakt:=(n,k)->expand(poch hammer(n-k+1,k)):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Delta(fallFakt(k,3),k);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(,&%\"kG\"\"\"F'F'F',&F&F'F'!\"\"F' F&F'F'*(F&F',&F&F'\"\"#F)F'F(F'F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "factor(Delta(fall Fakt(k,3),k));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"$\"\"\"%\"kG F&,&F'F&F&!\"\"F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "expand(fallFakt(k,3)+3*fallF akt(k,2)+fallFakt(k,1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"kG\" \"$\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "08." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 215 "summation:=proc(f,k)\nlocal i,n,g, st,lcoe;\ng:=f;\nn:=degree(g,k);\nst:=0;\nwhile n>0 do\n lcoe:=lcoeff (g,k);\n n:=degree(g,k);\n st:=st+lcoe*FallFakt(k,n+1)/(n+1);\n g:= expand(g-lcoe*fallFakt(k,n));\nend do;\nst\nend proc:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "09." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "summation(k^3,k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,(*&#\"\"\"\"\"%F&-%)FallFaktG6$%\"kGF'F&F&-F)6$F+\"\"$F&*&#F&\"\"#F&- F)6$F+F1F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "s:=factor(eval(subs(FallFakt=fallFa kt,summation(k^3,k))));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG,$*( \"\"%!\"\"%\"kG\"\"#,&F)\"\"\"F,F(F*F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "11." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "subs(k= n+1,s)-subs(k=1,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"%!\"\", &%\"nG\"\"\"F)F)\"\"#F(F*F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }