{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 "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 }} {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);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "expand(Delta(k^3,k));" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "fallFakt:=(n,k)->expand(pochhammer(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);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "factor(D elta(fallFakt(k,3),k));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "expand(fallFakt(k,3)+3*fall Fakt(k,2)+fallFakt(k,1));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "08. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 215 "summation:=proc(f,k)\n local 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);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "s:=factor(eva l(subs(FallFakt=fallFakt,summation(k^3,k))));" }}}{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);" }}}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }