{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 } {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 1 0 1 0 2 2 0 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 162 "Maple results of the arti cle\n\nB\366ing, H., Koepf, W.: Algorithms for q-Hypergeometric Summat ion in Computer Algebra, 1998, J. Symbolic Computation 28, 1999, 777-7 99" }}{PARA 0 "" 0 "" {TEXT -1 87 "\nThe timings were done on a Pentiu m processor i7-3820QM with 8GByte memory and 2,7 GHz." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "restart; read \"qsum 17.mpl\";" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%QPackage~\"q-Hypergeomet ric~Summation\",~Maple~V-17G" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#%epCop yright~1998-2013,~Harald~Boeing,~Wolfram~Koepf~&~Torsten~Sprenger,~Uni versity~of~KasselG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Section 2" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "result:=qgosper((1-a*p^k*q^k)/(1- a)/c^k*qpochhammer(a,p,k)/qpochhammer(a*p/c,p,k)*qpochhammer(c,q,k)/qp ochhammer(q,q,k),[p,q],k=0..n);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%' resultG*4-%,qpochhammerG6%%\"cG%\"qG,&%\"nG\"\"\"F-F-F--F'6%%\"aG%\"pG F+F-,&*&F0F-)F1F+F-F-F)!\"\"F-,&)F*F+F-F-F5F--F'6%F*F*F+F5-F'6%*(F0F-F 1F-F)F5F1F+F5)F),&F,F5F-F5F-,&F0F-F-F5F5,&F)F-F-F5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "qsimpcomb(result/qpochhammer(a*p,p,n)/qp ochhammer(c*q,q,n)*qpochhammer(a*p/c,p,n)*qpochhammer(q,q,n)*c^n);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^n) ^k,q,k,simplify=false);" }}{PARA 8 "" 1 "" {TEXT -1 63 "Error, (in qgo sper) No q-hypergeometric antidifference exists.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "qgosper(qpochhammer(a,q,k)/qpochhammer(q,q, k)/(a*q)^k,q,k,simplify=false);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*0, &)%\"qG%\"kG\"\"\"F(!\"\"F(F&F(%\"aGF(,&*,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( -%,qpochhammerG6%F*F&F'F(-F76%F&F&F'F))*&F&F(F*F(F'F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Table 1" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q, k)/(a*q^10)^k,q,k,simplify=false,solvemethod=solve): time()-TIME;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#Z!\"$" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 130 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/q pochhammer(q,q,k)/(a*q^20)^k,q,k,simplify=false,solvemethod=solve): ti me()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$c\"!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosper(qpoc hhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^10)^k,q,k,simplify=false,solvem ethod=gausselim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"# J!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): res ult:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^20)^k,q,k,simp lify=false,solvemethod=gausselim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#j!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q, k)/(a*q^30)^k,q,k,simplify=false,solvemethod=gausselim): time()-TIME; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$\\#!\"$" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosper(qpochhammer(a,q ,k)/qpochhammer(q,q,k)/(a*q^40)^k,q,k,simplify=false,solvemethod=gauss elim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$e)!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosp er(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^50)^k,q,k,simplify=false ,solvemethod=gausselim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%=Y!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=tim e(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^60)^k, q,k,simplify=false,solvemethod=gausselim): time()-TIME;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"&26\"!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpo chhammer(q,q,k)/(a*q^70)^k,q,k,simplify=false,solvemethod=gausselim): \+ time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&(f " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosp er(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^80)^k,q,k,simplify=false ,solvemethod=gausselim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&wF$!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=ti me(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^90)^k ,q,k,simplify=false,solvemethod=gausselim): time()-TIME;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"&(H\\!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpo chhammer(q,q,k)/(a*q^100)^k,q,k,simplify=false,solvemethod=gausselim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&65(!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosp er(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^10)^k,q,k,simplify=false ,solvemethod=ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" #y!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): re sult:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^20)^k,q,k,sim plify=false,solvemethod=ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#;!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q, k)/(a*q^30)^k,q,k,simplify=false,solvemethod=ABP): time()-TIME;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#Z!\"$" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/q pochhammer(q,q,k)/(a*q^40)^k,q,k,simplify=false,solvemethod=ABP): time ()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#$*!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosper(qpoc hhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^50)^k,q,k,simplify=false,solvem ethod=ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$(=!\"$ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:= qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^60)^k,q,k,simplify= false,solvemethod=ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"$\"G!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=tim e(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^70)^k, q,k,simplify=false,solvemethod=ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$o%!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q, k)/(a*q^80)^k,q,k,simplify=false,solvemethod=ABP): time()-TIME;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$L(!\"$" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/q pochhammer(q,q,k)/(a*q^90)^k,q,k,simplify=false,solvemethod=ABP): time ()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%-7!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "TIME:=time(): result:=qgosper(qpoc hhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^100)^k,q,k,simplify=false,solve method=ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%c=!\" $" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "t:=qbrackets(k,p)*qbra ckets(k,q)*qbrackets(k,r):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "result:=qsimpcomb(qgosper(subs(k=k+1,t)-t,[p,q,r],k));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'resultG**,0*()%\"pG%\"kG\"\"\")%\"qGF*F+) %\"rGF*F+F+*&F(F+F,F+!\"\"*&F(F+F.F+F1*&F,F+F.F+F1F(F+F,F+F.F+F+,&F)F+ F+F1F1,&F-F+F+F1F1,&F/F+F+F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "qsimpcomb(result-t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\" \"F$*(,&%\"pGF$F$!\"\"F$,&%\"qGF$F$F(F$,&%\"rGF$F$F(F$F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Section 3" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "qsumrecursion(qphihyperterm([a,b,q^(-n)],[c,a*b*q^(1-n)/c],q,q, k),q,k,S(n),rec2qhyper=true,sumrange=0..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$/-%\"SG6#%\"nG**-%,qpochhammerG6%*&%\"cG\"\"\"%\"bG! \"\"%\"qGF(F/-F+6%*&F.F/%\"aGF1F2F(F/-F+6%F.F2F(F1-F+6%*(F.F/F6F1F0F1F 2F(F11\"\"!F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "qsumrecurs ion(qphihyperterm([a,b,q^(-n)],[c,a*b*q^(1-n)/c],q,q,k),q,k,S(n),rec2q hyper=true);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$/-%\"SG6#%\"nG**-%,q pochhammerG6%*&%\"cG\"\"\"%\"bG!\"\"%\"qGF(F/-F+6%*&F.F/%\"aGF1F2F(F/- F+6%F.F2F(F1-F+6%*(F.F/F6F1F0F1F2F(F11\"\"!F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "qsumrecursion([a,b,q^(-n)],[c,a*b*q^(1-n)/c],q,q ,S(n),rec2qhyper=true,sumrange=0..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$/-%\"SG6#%\"nG**-%,qpochhammerG6%*&%\"cG\"\"\"%\"bG!\"\"%\"qGF(F/ -F+6%*&F.F/%\"aGF1F2F(F/-F+6%F.F2F(F1-F+6%*(F.F/F6F1F0F1F2F(F11\"\"!F( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "term:=_qsumrecursion_pr oof[_F];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%termG*0-%,qpochhammerG6 %%\"aG%\"qG%\"kG\"\"\"-F'6%%\"bGF*F+F,-F'6%)F*,$%\"nG!\"\"F*F+F,)F*F+F ,-F'6%%\"cGF*F+F5-F'6%**F)F,F/F,)F*,&F,F,F4F5F,F9F5F*F+F5-F'6%F*F*F+F5 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "RE:=_qsumrecursion_proo f[_recursion];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#REG/,&*(,&*&%\"cG \"\"\")%\"qG%\"nGF+F+F-!\"\"F+,&*(%\"aGF+%\"bGF+F-F+F/F)F+F+-%\"SG6#F. F+F+*(,&F)F+*&F3F+F-F+F/F+,&F)F+*&F-F+F2F+F/F+-F56#,&F.F+F+F/F+F/\"\"! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "cert:=_qsumrecursion_pr oof[_certificate];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%certG,$*.)%\" qG%\"nG\"\"\",&)F(%\"kGF*F*!\"\"F*,&*&%\"cGF*F,F*F*F(F.F*,&*(%\"aGF*% \"bGF*F(F*F.*&F1F*F'F*F*F*F,F.,&F'F*F*F.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "i:=_qsumrecursion_proof[_sumvar];" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"iG%\"kG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "result:=subs(\{S(n-1)=subs(n=n-1,term),S(n)=term\},lh s(RE))-(subs(i=i+1,cert*term)-cert*term):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 18 "qsimpcomb(result);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "term:=(-1)^k*q^ (k*(3*k-1)/2)*qbinomial(n+b,n+k,q)*qbinomial(n+c,c+k,q)*qbinomial(b+c, b+k,q):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "assume(n,integer ): sum2qhyper(term,q,k); n:='n':" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*0 )!\"\"%#n|irG\"\"\")%\"qG,$*(\"\"#F%F&F',&*&\"\"$F'F&F'F'F'F'F'F'F'-%, qpochhammerG6%F)F),&%\"cGF'F&F%F%-F16%F)F),$*&F,F'F&F'F'F%-F16%F)F),&% \"bGF'F4F'F'-F16%F)F),&F " 0 "" {MPLTEXT 1 0 40 "qDixon_RE :=qsumrecursion(term,q,k,S(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%* qDixon_REG/,**,,&)%\"qG%\"nG\"\"\"F,!\"\"F,,&)F*,$*&\"\"#F,F+F,F,F,F*F -F,)F*\"\"$F,,&F)F,F,F,F,-%\"SG6#F+F,F-*(,J)F*,**&\"\"%F,F+F,F,%\"bGF, %\"cGF,F2F,F,)F*,**&F>F,F+F,F,F?F,F@F,F,F,F,)F*,*F+F,F?F,F@F,F>F,F-)F* ,(*&F>F,F+F,F,F?F,F@F,F,)F*,(*&F4F,F+F,F,F?F,F2F,F-)F*,(*&F4F,F+F,F,F@ F,F2F,F-)F*,**&F2F,F+F,F,F?F,F@F,F2F,F-)F*,(*&F2F,F+F,F,F4F,F?F,F,)F*, (*&F2F,F+F,F,F4F,F@F,F,)F*,*F+F,F?F,F@F,F4F,F-)F*,&*&F4F,F+F,F,F2F,F-) F*,(*&F2F,F+F,F,F?F,F2F,F,)F*,(*&F2F,F+F,F,F@F,F2F,F,)F*,&*&F2F,F+F,F, F4F,F-)F*,(F+F,F?F,F4F,F-)F*,(F+F,F@F,F4F,F-*$)F*\"\"&F,F,)F*,&*&F4F,F +F,F,F,F,F-*$)F*F>F,F,*$F3F,F,F,F*F,-F76#,&F+F,F,F-F,F,*(,&)F*,(F+F,F? F,F@F,F,F*F-F,,B)F*,**&F4F,F+F,F,F?F,F@F,F2F,F,FDF,)F*,**&F4F,F+F,F,F? F,F@F,F,F,F,FRF-FUF-)F*,(F+F,F?F,F>F,F,)F*,(F+F,F@F,F>F,F,*$)F*\"\"'F, F-)F*,(*&F4F,F+F,F,F?F,F@F,F,FgnF-FjnF-F`oF,FboF,FdoF-)F*,&*&F2F,F+F,F ,F2F,F-FjoF-F,-F76#,&F+F,F2F-F,F-*,,&)F*,&F+F,F?F,F,*$)F*F2F,F-F,,&)F* ,&F+F,F@F,F,F_rF-F,,&FbpF,F_rF-F,FapF,-F76#,&F+F,F4F-F,F,\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "M:=qsimpcomb(subs(k=-k,term) /term);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG)%\"qG%\"kG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "qsumrecursion((1+M)/2*term,q ,k,S(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&,&)%\"qG%\"nG!\"\"\" \"\"F+F+-%\"SG6#F)F+F+*&,&)F(,(F)F+%\"bGF+%\"cGF+F+F+F*F+-F-6#,&F)F+F+ F*F+F+\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Table 2" }}{PARA 0 "" 0 "" {TEXT -1 8 "(III.18)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 390 "TI ME:=time():\nleftRE:=qsumrecursion(qpochhammer(a,q,k)*qpochhammer(a*q^ 2,q^2,k)*qpochhammer(b,q,k)*qpochhammer(c,q,k)*qpochhammer(d,q,k)*qpoc hhammer(e,q,k)*qpochhammer(q^(-n),q,k)*(a^2*q^(2+n)/(b*c*d*e))^k/(qpoc hhammer(a,q^2,k)*qpochhammer(a/b*q,q,k)*qpochhammer(a/c*q,q,k)*qpochha mmer(a/d*q,q,k)*qpochhammer(a/e*q,q,k)*qpochhammer(a*q^(n+1),q,k)*qpoc hhammer(q,q,k)),q,k,S(n));\ntime()-TIME;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'leftREG/,(*.%\"qG\"\"\",&*&)F(%\"nGF)%\"aGF)F)%\"eG!\"\"F),&F +F)%\"dGF0F),&F+F)%\"cGF0F),&F+F)%\"bGF0F)-%\"SG6#F-F)F)*(,B*&)F(,&*& \"\"$F)F-F)F)F)F)F))F.F@F)F)*.F4F)F2F)F/F))F(,$*&\"\"#F)F-F)F)F)F.F)F6 F)F0*&)F(,$*&F@F)F-F)F)F)FAF)F)*&)F(,&*&FFF)F-F)F)F)F)F)FAF)F0*(FLF))F .FFF)F6F)F0*(F4F)FLF)FPF)F0*(F2F)FLF)FPF)F0*(F/F)FLF)FPF)F0*,F4F)F2F)) F(,&F-F)F)F)F)F.F)F6F)F)*,F4F)F/F)FUF)F.F)F6F)F)*,F2F)F/F)FUF)F.F)F6F) F)*,F4F)F2F)F/F)FUF)F.F)F)*,F4F)F2F)F/F)FUF)F6F)F)*,F6F)F4F)F2F)F/F))F (FFF)F0*&)F(,&FFF)F-F)F)FPF)F)*,F6F)F4F)F2F)F/F)F(F)F0F),&F+F)F)F0F)-F 86#,&F-F)F)F0F)F0*,,&**F6F)F4F)F2F)F/F)F0*&F,F)FPF)F)F)F[oF),&F,F)F(F0 F),&F+F)F(F0F)-F86#,&F-F)FFF0F)F)\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#i!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 344 "TIME:=t ime():\nrightRE:=qsumrecursion(qpochhammer(a/(b*c)*q,q,k)*qpochhammer( d,q,k)*qpochhammer(e,q,k)*qpochhammer(q^(-n),q,k)*qpochhammer(a*q,q,n) *qpochhammer(a/(d*e)*q,q,n)*q^k/(qpochhammer(a/b*q,q,k)*qpochhammer(a/ c*q,q,k)*qpochhammer(d*e/a*q^(-n),q,k)*qpochhammer(q,q,k)*qpochhammer( a/d*q,q,n)*qpochhammer(a/e*q,q,n)),q,k,S(n));\ntime()-TIME;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(rightREG/,(*.%\"qG\"\"\",&*&)F(%\"nGF)%\" aGF)F)%\"eG!\"\"F),&F+F)%\"dGF0F),&F+F)%\"cGF0F),&F+F)%\"bGF0F)-%\"SG6 #F-F)F)*(,B*&)F(,&*&\"\"$F)F-F)F)F)F)F))F.F@F)F)*.F4F)F2F)F/F))F(,$*& \"\"#F)F-F)F)F)F.F)F6F)F0*&)F(,$*&F@F)F-F)F)F)FAF)F)*&)F(,&*&FFF)F-F)F )F)F)F)FAF)F0*(FLF))F.FFF)F6F)F0*(F4F)FLF)FPF)F0*(F2F)FLF)FPF)F0*(F/F) FLF)FPF)F0*,F4F)F2F))F(,&F-F)F)F)F)F.F)F6F)F)*,F4F)F/F)FUF)F.F)F6F)F)* ,F2F)F/F)FUF)F.F)F6F)F)*,F4F)F2F)F/F)FUF)F.F)F)*,F4F)F2F)F/F)FUF)F6F)F )*,F6F)F4F)F2F)F/F))F(FFF)F0*&)F(,&FFF)F-F)F)FPF)F)*,F6F)F4F)F2F)F/F)F (F)F0F),&F+F)F)F0F)-F86#,&F-F)F)F0F)F0*,,&**F6F)F4F)F2F)F/F)F0*&F,F)FP F)F)F)F[oF),&F,F)F(F0F),&F+F)F(F0F)-F86#,&F-F)FFF0F)F)\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#J!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "`recursion/compare`(leftRE,rightRE,S(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Recursions~are~identical.G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "(III.25)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 307 "c:=a^2*q/(b*d*lam):\nTIME:=time():\nleftRE:=qsumrecursion(qpoch hammer(a,q,k)*qpochhammer(b,q,k)*qpochhammer(c,q,k)*qpochhammer(d,q,k) *qpochhammer(q^(-n),q,k)*q^k/(qpochhammer(a/b*q,q,k)*qpochhammer(a/c*q ,q,k)*qpochhammer(a/d*q,q,k)*qpochhammer(a^2/lam^2*q^(-n),q,k)*qpochha mmer(q,q,k)),q,k,S(n)):\ntime()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#$*!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 590 "c:=a^2*q/ (b*d*lam):\nTIME:=time():\nrightRE:=qsumrecursion(qpochhammer(lam*q/a, q,n)*qpochhammer(lam^2*q/a,q,n)/qpochhammer(lam*q,q,n)/qpochhammer(lam ^2*q/a^2,q,n)*qpochhammer(lam,q,k)*qpochhammer(lam*q^2,q^2,k)*qpochham mer(b*lam/a,q,k)*qpochhammer(c*lam/a,q,k)*qpochhammer(d*lam/a,q,k)*qpo chhammer(a,q,2*k)*qpochhammer(lam^2/a*q^(n+1),q,k)*qpochhammer(q^(-n), q,k)*q^k/(qpochhammer(lam,q^2,k)*qpochhammer(a/b*q,q,k)*qpochhammer(a/ c*q,q,k)*qpochhammer(a/d*q,q,k)*qpochhammer(lam^2/a*q,q,2*k)*qpochhamm er(a/lam*q^(-n),q,k)*qpochhammer(lam*q^(n+1),q,k)*qpochhammer(q,q,k)), q,k,S(n)):\ntime()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$]#!\"$ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "`recursion/compare`(lef tRE,rightRE,S(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Recursions~are ~identical.G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "(III.28)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 499 "c:=a^2*q/(b*d*lam):\nTIME:=time():\nleft RE:=qsumrecursion(qpochhammer(a,q,k)*qpochhammer(a*q^2,q^2,k)*qpochham mer(b,q,k)*qpochhammer(c,q,k)*qpochhammer(d,q,k)*qpochhammer(e,q,k)*qp ochhammer(f,q,k)*qpochhammer(lam*a/(e*f)*q^(n+1),q,k)*qpochhammer(q^(- n),q,k)*q^k/(qpochhammer(a,q^2,k)*qpochhammer(a/b*q,q,k)*qpochhammer(a /c*q,q,k)*qpochhammer(a/d*q,q,k)*qpochhammer(a/e*q,q,k)*qpochhammer(a/ f*q,q,k)*qpochhammer(e*f/lam*q^(-n),q,k)*qpochhammer(a*q^(n+1),q,k)*qp ochhammer(q,q,k)),q,k,S(n)):\ntime()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$m#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 732 "c:=a^2*q/(b*d*lam):\nTIME:=time():\nrightRE:=qsumrecursion(qpochh ammer(lam,q,k)*qpochhammer(lam*q^2,q^2,k)*qpochhammer(b*lam/a,q,k)*qpo chhammer(c*lam/a,q,k)*qpochhammer(d*lam/a,q,k)*qpochhammer(e,q,k)*qpoc hhammer(f,q,k)*qpochhammer(lam*a/(e*f)*q^(n+1),q,k)*qpochhammer(q^(-n) ,q,k)*q^k*qpochhammer(a*q,q,n)*qpochhammer(a/(e*f)*q,q,n)*qpochhammer( lam/e*q,q,n)*qpochhammer(lam/f*q,q,n)/(qpochhammer(lam,q^2,k)*qpochham mer(a/b*q,q,k)*qpochhammer(a/c*q,q,k)*qpochhammer(a/d*q,q,k)*qpochhamm er(lam/e*q,q,k)*qpochhammer(lam/f*q,q,k)*qpochhammer(e*f/a*q^(-n),q,k) *qpochhammer(lam*q^(n+1),q,k)*qpochhammer(q,q,k)*qpochhammer(a/e*q,q,n )*qpochhammer(a/f*q,q,n)*qpochhammer(lam/(e*f)*q,q,n)*qpochhammer(lam* q,q,n)),q,k,S(n)):\ntime()-TIME; c:='c':" }{TEXT -1 0 "" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"$(=!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "`recursion/compare`(leftRE,rightRE,S(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Recursions~are~identical.G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Little " }{XPPEDIT 18 0 "q" "6#%\"qG" } {TEXT -1 10 "-Legendre:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "qsumrecu rsion([q^(-n),q^(n+1)],[q],q,q*x,p(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/,(**)%\"qG%\"nG\"\"\",&F&F)F)!\"\"F),&F&F)F'F)F)-%\"pG6#F(F)F)* (,,*&%\"xGF))F',$*&\"\"#F)F(F)F)F)F)*&F3F))F',&F(F)F)F)F)F)*&F&F)F3F)F )*&F'F)F3F)F)*&F7F)F&F)F+F),&F4F)F'F+F)-F.6#,&F(F)F)F+F)F)**,&F&F)F)F) F),&F&F)F'F+F)F&F)-F.6#,&F(F)F7F+F)F)\"\"!" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 49 "qsumrecursion([q^(-n),q^(n+1)],[q],q,q*q^y,p(y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*(,&)%\"qG%\"yG\"\"\"F*!\"\"F*)F( ,&%\"nGF*F*F*F*-%\"pG6#F)F*F**&,()F(,(F)F**&\"\"#F*F.F*F*F*F*F+*&F7F*F ,F*F*F'F+F*-F06#,&F)F*F*F+F*F**(,&F'F*F(F+F*)F(F.F*-F06#,&F)F*F7F+F*F* \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "qsumdiffeq([q^(-n) ,q^(n+1)],[q],q,q*x,p(x));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/,(**%\" qG\"\"\",&)F&%\"nGF'F'!\"\"F',&*&F)F'F&F'F'F'F+F'-%\"pG6#%\"xGF'F'*(,& F&F'F'F+F',.*()F)\"\"#F')F&F7F'F1F'F'*(F)F')F&\"\"$F'F1F'F+*(F8F'F1F'F )F'F+F-F'*&F&F'F1F'F'F)F+F'-&%#DqGF06#F.F'F'*.F)F',&*&F8F'F1F'F'F'F+F' F1F')F3F7F'F&F'-&F@6$F1F1FAF'F+\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "qsumrecursion([q^(-n),q^(n+1)],[q],q,q,p(n),rec2qhype r=true);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$/-%\"pG6#%\"nG*&),$%\"qG !\"\"F(\"\"\")F,-%)binomialG6$F(\"\"#F.1\"\"!F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Al-Salam-Chihara polynomials" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "re1:= qsumrecursion(qpochhammer(a*b,q,n)/a^n,\n[q^(- n),a*exp(I*theta),a*exp(-I*theta)],[a*b,0],q,q,Q(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$re1G/,(*(-%$expG6#*&%&thetaG\"\"\"^#F-F-F-)%\"q G\"\"$F--%\"QG6#%\"nGF-F-*(,**()F0F5F-%\"aGF-F(F-F-*(F9F-%\"bGF-F(F-F- *&F0F-)F(\"\"#F-!\"\"F0F@F-)F0F?F--F36#,&F5F-F-F@F-F-**F(F-,&*(F:F-F " 0 "" {MPLTEXT 1 0 155 "re2:= qsumrecursion(qpochhammer(b* exp(-I*theta),q,n)*exp(I*n*theta),\n[q^(-n),a*exp(I*theta)],[b^(-1)*q^ (1-n)*exp(I*theta)],\nq,b^(-1)*q*exp(-I*theta),Q(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$re2G/,(*(-%$expG6#*&%&thetaG\"\"\"^#F-F-F-)%\"q G\"\"$F--%\"QG6#%\"nGF-F-*(,**()F0F5F-%\"aGF-F(F-F-*(F9F-%\"bGF-F(F-F- *&F0F-)F(\"\"#F-!\"\"F0F@F-)F0F?F--F36#,&F5F-F-F@F-F-**F(F-,&*(F:F-F " 0 "" {MPLTEXT 1 0 34 "`recursion/compare`(re1,re2,Q(n)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Recursions~are~identical.G" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Askey-Wilson polynomials" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 362 "c:= (k,n,a,b,c,d,alpha,beta,gamma,j) -> \nqpochhammer(alpha*d,beta*d,gamma*d,q,q,n)*qpochhammer(alpha*beta*gam ma*d*q^(n-1),q,k)/qpochhammer(alpha*d,beta*d,gamma*d,q,a*b*c*d*q^(k-1) ,q,k)/qpochhammer(q,q,n-k)*q^(k^2-n*k)*d^(k-n)*qphihyperterm([q^(k-n), alpha*beta*gamma*d*q^(n+k-1),a*d*q^k,b*d*q^k,c*d*q^k],[a*b*c*d*q^(2*k) ,alpha*d*q^k,beta*d*q^k,gamma*d*q^k],q,q,j);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"cGf*6,%\"kG%\"nG%\"aG%\"bGF$%\"dG%&alphaG%%betaG%&g ammaG%\"jG6\"6$%)operatorG%&arrowGF0*0-%,qpochhammerG6(*&9*\"\"\"9)F:* &9+F:F;F:*&9,F:F;F:%\"qGF@9%F:-F66%*,F9F:F=F:F?F:F;F:)F@,&FAF:F:!\"\"F :F@9$F:-F66)F8FF@*,9&F:9'F:9(F:F;F:)F@,&FHF:F:FGF:F@FHFG-F66%F@F@,& FAF:FHFGFG)F@,&*$)FH\"\"#F:F:*&FAF:FHF:FGF:)F;,&FHF:FAFGF:-%.qphihyper termG6'7')F@Fen*,F9F:F=F:F?F:F;F:)F@,(FAF:FHF:F:FGF:*(FLF:F;F:)F@FHF:* (FMF:F;F:F_oF:*(FNF:F;F:F_oF:7&*,FLF:FMF:FNF:F;F:)F@,$*&FXF:FHF:F:F:*( F9F:F;F:F_oF:*(F=F:F;F:F_oF:*(F?F:F;F:F_oF:F@F@9-F:F0F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "intermediate:=qsumrecursion(c(k,N+ k,a,b,c,d,alpha,b,c,j),q,j,S(N),rec2qhyper=true,sumrange=0..N):\nfinal := subs(N=n-k,rhs(intermediate[1]));" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#>%&finalG*B,&*,%\"cG\"\"\"%\"dGF))%\"qG%\"kGF)%\"bGF)%&alphaGF)F)F,! \"\"F)-%,qpochhammerG6%F'F,F-F),&*,%\"aGF)F.F)F(F)F*F))F+\"\"#F)F)F,F0 F),&*,F(F)F*F)F7F)F.F)F/F)F)F,F0F0,&*,F6F)F.F)F(F)F*F)F+F)F)F,F0F0-F26 %F " 0 "" {MPLTEXT 1 0 228 "RHS:=qpochhammer(alpha/a,q,n-k)*qpochhammer(alpha*b* c*d*q^(n-1),q,k)*qpochhammer(b*c,b*d,c*d,q,n)*a^(n-k)*qpochhammer(q,q, n)/(qpochhammer(q,b*c,b*d,c*d,q,k)*qpochhammer(a*b*c*d*q^(k-1),q,k)*qp ochhammer(q,a*b*c*d*q^(2*k),q,n-k));" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#>%$RHSG*>-%,qpochhammerG6%*&%&alphaG\"\"\"%\"aG!\"\"%\"qG,&%\"nGF+% \"kGF-F+-F'6%*,F*F+%\"bGF+%\"cGF+%\"dGF+)F.,&F0F+F+F-F+F.F1F+-F'6%*&F5 F+F6F+F.F0F+-F'6%*&F5F+F7F+F.F0F+-F'6%*&F6F+F7F+F.F0F+)F,F/F+-F'6%F.F. F0F+-F'6%F.F.F1F--F'6%F " 0 "" {MPLTEXT 1 0 21 "qsimpcomb(final/RHS);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*F-%,qpochhammerG6%*,%\"cG\"\"\"%\"dGF))%\"qG%\"kGF)%\"bGF)%&alp haGF)F,F-F)-F%6%*(F(F)F+F)F.F)F,,&%\"nGF)F-!\"\"F)-F%6%*,F(F)F*F))F+\" \"#F)F.F)F/F)F,F3F)-F%6%*(F.F)F*F)F+F)F,F3F)-F%6%*(F(F)F*F)F+F)F,F3F), &)F,F4F)F)F5F)-F%6%F+F,F3F)-F%6%F,F,F-F)-F%6%*&F.F)F(F)F,F-F)-F%6%*&F. F)F*F)F,F-F)-F%6%*&F(F)F*F)F,F-F)-F%6%F,F,F4F5-F%6%FOF,F4F5-F%6%FLF,F4 F5-F%6%FIF,F4F5-F%6%*,F/F)F.F)F(F)F*F)FBF)F,F-F5-F%6%F'F,F3F5,&F+F)F)F 5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "qsimplify(final/RHS) ;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*:-%,qpochhammerG6%*,%\"cG\"\"\"% \"dGF)%\"qG!\"\"%\"aGF)%\"bGF)F+,$*&\"\"#F)%\"kGF)F)F)-F%6%F'F+F2F,-F% 6%*,F(F)F*F)F+F,F.F)%&alphaGF)F+F2F)-F%6%F7F+F/F,,&*,F(F)F*F))F+F2F)F. F)F8F)F)F+F,F),&*,F(F)F*F))F=F1F)F.F)F8F)F)F+F,F,-F%6%**F-F)F.F)F(F)F* F)F+F/F,-F%6%FCF+F2F)-F%6%**F8F)F.F)F(F)F*F)F+F2F,-F%6%FHF+F/F),&*,F-F )F.F)F(F)F*F)F=F)F)F+F,F,,&*,F-F)F.F)F(F)F*F)F@F)F)F+F,F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "qratio(final/RHS,k);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "eval(subs(k=0,final/RHS));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\" \"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "RE2:=qsumrecursion (c(k,N+k,a,b,c,d,a,beta,c,j),q,j,S(N),rec2qhyper=true):\nfinal2:= subs (N=n-k,rhs(RE2[1]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'final2G*B,& *,%%betaG\"\"\"%\"cGF)%\"dGF))%\"qG%\"kGF)%\"aGF)F)F-!\"\"F)-%,qpochha mmerG6%F'F-F.F),&*,F/F)%\"bGF)F*F)F+F))F,\"\"#F)F)F-F0F),&*,F(F)F*F)F+ F)F7F)F/F)F)F-F0F0,&*,F/F)F6F)F*F)F+F)F,F)F)F-F0F0-F26%F " 0 "" {MPLTEXT 1 0 108 "RE3: =qsumrecursion(c(k,N+k,a,b,c,d,a,b,gamma,j),q,j,S(N),rec2qhyper=true): \nfinal3:= subs(N=n-k,rhs(RE3[1]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #>%'final3G*B,&*,%\"dG\"\"\"%&gammaGF))%\"qG%\"kGF)%\"aGF)%\"bGF)F)F,! \"\"F)-%,qpochhammerG6%F'F,F-F),&*,F.F)F/F)%\"cGF)F(F))F+\"\"#F)F)F,F0 F),&*,F(F)F*F)F7F)F.F)F/F)F)F,F0F0,&*,F.F)F/F)F6F)F(F)F+F)F)F,F0F0-F26 %F " 0 "" {MPLTEXT 1 0 82 "TIME:=time(): Sn :=qrecsolve(qDixon_RE,q,S(n),output=qhypergeometric);\ntime()-TIME;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#SnG7#7$*&-%,qpochhammerG6%)%\"qG,( %\"bG\"\"\"%\"cGF/F/F/F,%\"nGF/-F)6%F,F,F1!\"\"1\"\"!F1" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"%.T!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "TIME:=time(): Sn:=qrecsolve(qDixon_RE,q,S(n),output=q hypergeometric,split=false);\ntime()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#SnG7#7$*&-%,qpochhammerG6%)%\"qG,(%\"bG\"\"\"%\"cGF/ F/F/F,%\"nGF/-F)6%F,F,F1!\"\"1\"\"!F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%W:!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "qsimplify (Sn[1][1]*qpochhammer(q,q,n)*qpochhammer(q,q,b)*qpochhammer(q,q,c)/qpo chhammer(q,q,n+b+c));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%,qpochham merG6%*&%\"qG\"\"\")F(%\"cGF)F(%\"bG!\"\"-F%6%F(F(F,F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 191 "qrecsolve(q^k*(q+1)*(q-1)*(q^(k+1) -1)*F(k+2)+(q+1)*(1-q^(k+1))*(q^k*(a*q-a)+a-1)*F(k+1)+(a+1)*(a-1)*(q^( k+1)-1)*F(k)=(a-1)*(a-q)*(q^k+1)*(q^k-1)*qpochhammer(a,q,k)/qpochhamme r(q,q,k),q,F(k));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#,$*(,&)%\"qG%\" kG\"\"\"F*!\"\"F*-%,qpochhammerG6%%\"aGF(F)F*-F-6%F(F(F)F+F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "qrecsolve(q^2*q^(2*n)*F(n+3) +(1+q)*q^n*F(n+2)+(1-q^n)*F(n+1)-F(n),q,F(n),solution=series);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7#-%$SumG6$*(-%,qpochhammerG6%%\"qGF+% #_iG!\"\"%$_C1G\"\"\")F+,&*$)F,\"\"#F/F/*&F,F/%\"nGF/F/F//F,;\"\"!%)in finityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "qrecsolve((a*q^k -1)*X(k)-a*q^n*(q^k-1)*X(k-1)=1,q,X(k),solution=series);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7#-%$SumG6$,$**)%\"qG,&*&%#_iG\"\"\"%\"kGF.F.F-F .F.-%,qpochhammerG6%*&)F*,$%\"nG!\"\"F.%\"aGF7F*F-F7-F16%F4F*F-F.,&*&) F*F6F.F8F.F7)F*F-F.F7F7/F-;\"\"!%)infinityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "assume(n,posint);\nqgosper(qpochhammer(a,q,k)/qpoc hhammer(q,q,k)/(a*q^n)^k,q,k,series=true);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*0,&)%\"qG%\"kG\"\"\"F(!\"\"F()F&%#n|irGF(%\"aGF(-%$Sum G6$**-%,qpochhammerG6%)F&,$F+F)F&%#_iGF()F&*&F6F(F'F(F(,&*&F*F(F,F(F() F&F6F)F)-F26%*&F4F(F,F)F&F6F)/F6;\"\"!F+F(-F26%F,F&F'F(-F26%F&F&F'F))F :,$F'F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "61 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }