{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 200 3 "01." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "pochhammer(1/2,k);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "with(gf un):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 543 "HolonomicRE:=proc( a,Ak)\nlocal A,k,rat,re,i;\nif type(a,`+`)\n then re:=HolonomicRE(op( 1,a),Ak);\n for i from 1 to nops(a)-1 do\n re:=`rec+rec` (re,HolonomicRE(op(i+1,a),Ak),Ak);\n end do;\n return re; \nend if;\nif type(a,`*`)\n then re:=HolonomicRE(op(1,a),Ak);\n \+ for i from 1 to nops(a)-1 do\n re:=`rec*rec`(re,HolonomicRE(o p(i+1,a),Ak),Ak);\n end do;\n return re;\nend if;\nA:=op(0 ,Ak);\nk:=op(1,Ak);\nrat:=normal(expand(subs(k=k+1,a)/a));\ncollect(A( k+1)*denom(rat)-A(k)*numer(rat),A(k),factor);\nend proc:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "03." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "[HolonomicRE(pochhammer(1/2,k),a(k)),simplify(subs(k= 0,pochhammer(1/2,k)))];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "04." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "[HolonomicRE((2*k)!/(4^k*k !),a(k)),simplify(subs(k=0,(2*k)!/(4^k*k!)))];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "po chhammer(1/2,k);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "06." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "HolonomicRE(binomial(n,k),a( k));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "07." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "RE1:=op(3,HolonomicRE(binomial(n-1,k)+binomia l(n-1,k-1),a(k)));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "08." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "applyrule(a(k::anything)=bin omial(n,k),RE1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "09." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "evalb(simplify(expand(applyr ule(a(k::anything)=binomial(n,k),RE1)=0)));" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 200 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "appl yrule([binomial(n::anything,k::negint)=0,binomial(n::anything,0)=1],ev al(subs(k=0,[binomial(n,k),binomial(n-1,k)+binomial(n-1,k-1)])));" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "11." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "eval(subs(k=1,[binomial(n,k),binomial(n-1,k)+binomial (n-1,k-1)]));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "12." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "RE2:=op(2,HolonomicRE(binomial(n-1, k)+binomial(n-1,k-1),a(n)));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "1 3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "evalb(simplify(expand (applyrule(a(n::anything)=binomial(n,k),RE2)))=0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "14." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "eval(subs([k=1,n=1],[binomial(n,k),binomial(n-1,k)+binomial(n-1,k-1)] ));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "15." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 72 "eval(subs([k=1,n=2],[binomial(n,k),binomial(n- 1,k)+binomial(n-1,k-1)]));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "16. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "eval(subs([k=2,n=1],[bi nomial(n,k),binomial(n-1,k)+binomial(n-1,k-1)]));" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 200 3 "17." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 " eval(subs([k=2,n=2],[binomial(n,k),binomial(n-1,k)+binomial(n-1,k-1)]) );" }}}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }