{VERSION 3 0 "IBM INTEL NT" "3.0" } {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 "Times" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 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 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 0 0 0 2 1 2 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "P:=sum(alpha[M-l]*n^l,l=M-2..M):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Q:=sum(beta[M-l]*n^l,l=M-2 ..M):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "R:=sum(gamma[M-l]* n^l,l=M-2..M):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "s:=sum(de lta[N-l]*n^l,l=N-2..N):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " term:=expand(P*subs(n=n+2,s)+Q*subs(n=n+1,s)+R*s):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "term:=expand(subs((n+1)^N=n^N+N*n^(N-1)+N*( N-1)/2*n^(N-2),term)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "t erm:=expand(subs((n+2)^N=n^N+2*N*n^(N-1)+4*N*(N-1)/2*n^(N-2),term)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "term:=numer(normal(term/( n^M*n^N))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "term:=collec t(term,n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "deg:=degree(t erm,n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "eq1:=factor(coef f(term,n,deg));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G,$*&&%&delta G6#\"\"!\"\"\",(&%&alphaGF)F+&%&gammaGF)F+&%%betaGF)F+F+\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "eq1:=normal(eq1/(2*delta[0]) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G,(&%&alphaG6#\"\"!\"\"\"& %&gammaGF(F*&%%betaGF(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "alpha[0]:=solve(eq1,alpha[0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&% &alphaG6#\"\"!,&&%&gammaGF&!\"\"&%%betaGF&F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "eq2:=factor(coeff(term,n,deg-1));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$eq2G,$*&&%&deltaG6#\"\"!\"\"\",,&%&alphaG6#F+ F+&%&gammaGF/F+*&%\"NGF+&F1F)F+!\"#*&&%%betaGF)F+F3\"\"\"!\"\"&F8F/F+F +\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "eq2:=collect(norm al(eq2/(2*delta[0])),N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G,** &,&&%&gammaG6#\"\"!!\"#&%%betaGF*!\"\"\"\"\"%\"NGF0F0&%&alphaG6#F0F0&F )F4F0&F.F4F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "alpha[1]:=s olve(coeff(eq2,N,0),alpha[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%& alphaG6#\"\"\",&&%&gammaGF&!\"\"&%%betaGF&F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "beta[0]:=solve(coeff(eq2,N,1),beta[0]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%betaG6#\"\"!,$&%&gammaGF&!\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "eq3:=factor(coeff(term,n,deg -2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq3G,$*&&%&deltaG6#\"\"!\" \"\",0&%&alphaG6#\"\"#F+&%&gammaGF/F+&%%betaGF/F+*&&F46#F+F+%\"NGF+!\" \"*&F8\"\"\"&F2F7F+!\"#*&&F2F)F+)F8F0F;F+*&F8F;F?F;F9F+F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "eq3:=collect(normal(eq3/(2*delta[0] )),N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq3G,,*&&%&gammaG6#\"\"! \"\"\")%\"NG\"\"#\"\"\"F+*&,(&%%betaG6#F+!\"\"&F(F4!\"#F'F5F+F-F+F+&%& alphaG6#F.F+&F(F:F+&F3F:F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "P:=n*(n+1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Q:=-2*n* (n+100):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "R:=(n+99)*(n+10 0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "s:=sum(delta[100-l]* n^l,l=0..100):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "rec:=coll ect(P*subs(n=n+2,s)+Q*subs(n=n+1,s)+R*s,n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "sol:=solve(\{coeffs(rec,n)\},\{seq(delta[l],l=0..1 00)\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "factor(subs(sol, s));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*dw%\"nG\"\"\",&F$\"\"\"\"#)*F 'F',&F$F'\"#(*F'F',&F$F'\"#'*F'F',&F$F'\"#&*F'F',&F$F'\"#%*F'F',&F$F' \"#$*F'F',&F$F'\"##*F'F',&F$F'\"#\"*F'F',&F$F'\"#!*F'F',&F$F'\"#*)F'F' ,&F$F'\"#))F'F',&F$F'\"#()F'F',&F$F'\"#')F'F',&F$F'\"#&)F'F',&F$F'\"#% )F'F',&F$F'\"#$)F'F',&F$F'\"##)F'F',&F$F'\"#\")F'F',&F$F'\"#!)F'F',&F$ F'\"#zF'F',&F$F'\"#yF'F',&F$F'\"#xF'F',&F$F'\"#wF'F',&F$F'\"#vF'F',&F$ F'\"#uF'F',&F$F'\"#tF'F',&F$F'\"#sF'F',&F$F'\"#rF'F',&F$F'\"#qF'F',&F$ F'\"#pF'F',&F$F'\"#oF'F',&F$F'\"#nF'F',&F$F'\"#mF'F',&F$F'\"#lF'F',&F$ F'\"#kF'F',&F$F'\"#jF'F',&F$F'\"#iF'F',&F$F'\"#hF'F',&F$F'\"#gF'F',&F$ F'\"#fF'F',&F$F'\"#eF'F',&F$F'\"#dF'F',&F$F'\"#cF'F',&F$F'\"#bF'F',&F$ F'\"#aF'F',&F$F'\"#`F'F',&F$F'\"#_F'F',&F$F'\"#^F'F',&F$F'\"#]F'F',&F$ F'\"#\\F'F',&F$F'\"#[F'F',&F$F'\"#ZF'F',&F$F'\"#YF'F',&F$F'\"#XF'F',&F $F'\"#WF'F',&F$F'\"#VF'F',&F$F'\"#UF'F',&F$F'\"#TF'F',&F$F'\"#SF'F',&F $F'\"#RF'F',&F$F'\"#QF'F',&F$F'\"#PF'F',&F$F'\"#OF'F',&F$F'\"#NF'F',&F $F'\"#MF'F',&F$F'\"#LF'F',&F$F'\"#KF'F',&F$F'\"#JF'F',&F$F'\"#IF'F',&F $F'\"#HF'F',&F$F'\"#GF'F',&F$F'\"#FF'F',&F$F'\"#EF'F',&F$F'\"#DF'F',&F $F'\"#CF'F',&F$F'\"#BF'F',&F$F'\"#AF'F',&F$F'\"#@F'F',&F$F'\"#?F'F',&F $F'\"#>F'F',&F$F'\"#=F'F',&F$F'\"# " 0 "" {MPLTEXT 1 0 36 "read `c:/koepf/maple/buch/hsum.mpl`;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%ZCopyright~1998~~Wolfram~Koepf,~Konrad-Zuse-Zentr um~BerlinG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "s:='s': rec2 poly(n*(n+1)*s(n+2)-2*n*(n+10)*s(n+1)+(n+9)*(n+10)*s(n),s(n));" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#*6%\"nG\"\"\",&F$\"\"\"\"\")F'F',&F$F' \"\"(F'F',&F$F'\"\"'F'F',&F$F'\"\"&F'F',&F$F'\"\"%F'F',&F$F'\"\"$F'F', &F$F'\"\"#F'F',&F$F'F'F'F',(*&F$F'&%&deltaG6#\"\"!F'F'&F96#F'F'F8!#OF' " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "rec2poly(n*(n+1)*s(n+2) -2*n*(n+20)*s(n+1)+(n+19)*(n+20)*s(n),s(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*J%\"nG\"\"\",&F$\"\"\"\"#=F'F',&F$F'\"# " 0 "" {MPLTEXT 1 0 34 "P:=n+4: Q:=1: R:=-n-1: q:=1: r:=1: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "\{solve(lcoeff(collect (C^2*normal(P/subs(n=n+2,r))*subs(n=n+2,q)+C*Q+normal(R/subs(n=n+1,q)) *subs(n=n+1,r),n),n),C)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$!\"\" \"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "C:=-1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "pol:=rec2poly(C^2*normal(P/subs(n= n+2,r))*p(n+2)*subs(n=n+2,q)+C*Q*p(n+1)+normal(R/subs(n=n+1,q))*p(n)*s ubs(n=n+1,r),p(n));" }}{PARA 8 "" 1 "" {TEXT -1 50 "Error, (in rec2pol y) no polynomial solution exists" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "p ol:=rec2poly(C^2*normal(P/subs(n=n+2,r))*p(n+2)*subs(n=n+2,q)+C*Q*p(n+ 1)+normal(R/subs(n=n+1,q))*p(n)*subs(n=n+1,r),p(n));" }}{PARA 8 "" 1 " " {TEXT -1 50 "Error, (in rec2poly) no polynomial solution exists" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "q:=n: C:='C':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "\{solve(lcoeff(collect(C^2*normal( P/subs(n=n+2,r))*subs(n=n+2,q)+C*Q+normal(R/subs(n=n+1,q))*subs(n=n+1, r),n),n),C)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C:=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "pol:=rec2poly(C^2*normal(P/subs(n=n+2,r))*p(n+2)*sub s(n=n+2,q)+C*Q*p(n+1)+normal(R/subs(n=n+1,q))*p(n)*subs(n=n+1,r),p(n)) ;" }}{PARA 8 "" 1 "" {TEXT -1 50 "Error, (in rec2poly) no polynomial s olution exists" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "q:=1: r:= n+2: C:='C':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "\{solve(lc oeff(collect(C^2*normal(P/subs(n=n+2,r))*subs(n=n+2,q)+C*Q+normal(R/su bs(n=n+1,q))*subs(n=n+1,r),n),n),C)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "q:=n: " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "\{solve(lcoeff(collect(C^2* normal(P/subs(n=n+2,r))*subs(n=n+2,q)+C*Q+normal(R/subs(n=n+1,q))*subs (n=n+1,r),n),n),C)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$!\"\"\"\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "C:=-1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "pol:=rec2poly(C^2*normal(P/subs(n=n+2,r) )*p(n+2)*subs(n=n+2,q)+C*Q*p(n+1)+normal(R/subs(n=n+1,q))*p(n)*subs(n= n+1,r),p(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG,$*&&%&deltaG6 #\"\"!\"\"\",&\"\"$F+%\"nG\"\"#F+#F+F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "t:=normal(C*subs(n=n+1,pol)*subs(n=n+1,q)/(pol*subs(n =n+1,r)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tG,$*&*&,&\"\"&\"\" \"%\"nG\"\"#F*,&F+F*F*F*F*\"\"\"*&,&\"\"$F*F+F,\"\"\",&F+F*F1F*\"\"\"! \"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C:=1:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "pol:=rec2poly(C^2*normal(P/ subs(n=n+2,r))*p(n+2)*subs(n=n+2,q)+C*Q*p(n+1)+normal(R/subs(n=n+1,q)) *p(n)*subs(n=n+1,r),p(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG& %&deltaG6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "t:=norma l(C*subs(n=n+1,pol)*subs(n=n+1,q)/(pol*subs(n=n+1,r)));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"tG*&,&%\"nG\"\"\"F(F(\"\"\",&F'F(\"\"$F(!\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "rec:=sumrecursion((-1 )^k*binomial(n,k)*binomial(3*k,n),k,s(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$recG/,(*&,&\"\"$\"\"\"%\"nG\"\"#F*-%\"sG6#,&F+F*F,F* F*F,*&,&F+\"\"&\"\"(F*F*-F.6#,&F+F*F*F*F*F)*&F7F*-F.6#F+F*\"\"*\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "rec2hyper(rec,s(n));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "rec2hyper((n+4)*s(n+2)+s(n+1)-(n+1)*s(n),s(n));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "rec2hyper(2*(2*n+3)*s(n+2)+3*(5*n+7)*s(n+1)+9*s(n)*(n +1),s(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "rec2hyper((n+1)^3*s(n)-(2*n+3)*(17*n^2+51 *n+39)*s(n+1)+s(n+2)*(n+2)^3,s(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #<\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "rec2hyper(2*n*(1+n) *s(n)+(2-3*n-n^2)*s(n+1)+(n-1)*s(n+2),s(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$\"\"#,&%\"nG\"\"\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "rec2hyper(s(n+2)-(n+1)*s(n+1)-(n+1)*s(n),s(n));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "rec2hyper(81*(2+3*n)*(4+3*n)*s(n)-6*(70+99*n+36*n^2)* s(n+1)+8*(2+n)*(3+2*n)*s(n+2),s(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#<##\"#F\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "rec2hyper (9*(n+2)*s(n+2)-3*(n+4)*s(n+1)-2*(n+3)*s(n),s(n));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#<$#!\"\"\"\"$,$*&,&\"\"(\"\"\"%\"nGF&\"\"\",&\"\"%F+F ,F&!\"\"#\"\"#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "read `c :/koepf/maple/buch/qsum.mpl`;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%OCop yright~1998,~~Harald~Boeing~&~Wolfram~KoepfG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%;Konrad-Zuse-Zentrum~BerlinG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "q:='q':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "q -Chu-Vandermonde" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "RE:=qfasenmyer( qphihyperterm([q^(-n),b],[c],q,c/q^(-n)/b,k),q,k,S(n),1,2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#REG/,(**%\"bG\"\"\"%\"qGF),&*&)F*%\"nGF)% \"cGF)F)F*!\"\"F)-%\"SG6#F.F)F)*&,.*&)F*\"\"$\"\"\"F(F9F)*()F*,&F.F)F) F)F)F/F9F(F9F0*&)F*,&F.F)\"\"#F)F)F(F9F0*&)F*F@F9F(F9F)*&F;F9F/F9F0*() F*,$F.F@F)F/F9F(F9F)F)-F26#,&F.F)F0F)F)F)*(,&F-F0F*F)F),&FAF)F,F0F)-F2 6#,&F.F)!\"#F)F)F0\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " qrecsolve(RE,q,S(n),return=qhypergeometric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7$*&-%,qpochhammerG6%*&%\"cG\"\"\"%\"bG!\"\"%\"qG%\"n GF+-F'6%F*F.F/F-1\"\"!F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "qrecsolve(RE,q,S(n),return=uprec);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #7#7#/,&*(%\"bG\"\"\",&*&)%\"qG%\"nGF)%\"cGF)F)!\"\"F)F)-%\"SG6#,&F.F) F)F)F)F)*&,&F+F)F(F0F)-F26#F.F)F0\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "comparison with q-Zeilberger algorithm" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "qsumrecursion(qphihyperterm([q^(-n),b],[c],q,c/q^( -n)/b,k),q,k,S(n),recursion=up);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/, &*(,&*&)%\"qG%\"nG\"\"\"%\"cGF+F+!\"\"F+F+%\"bGF+-%\"SG6#,&F*F+F+F+F+F +*&,&F'F-F.F+F+-F06#F*F+F+\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }