{VERSION 4 0 "SUN SPARC SOLARIS" "4.0" } {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 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }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 3 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "W arning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 1 } 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 1 }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 1 }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 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 145 "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," }}{PARA 0 "" 0 "" {TEXT -1 10 "to appear." }}{PARA 0 "" 0 "" {TEXT -1 52 "\nThe tim ings were done on a Pentium PC with 200 MHz." }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "restart; read `qsum6.mpl`;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%NPackage~\"q-Hypergeometric~Summati on\",~Maple~6G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%^oCopyright~2001,~H arald~Boeing~&~Wolfram~Koepf,~University~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)/qpochhamme r(a*p/c,p,k)*qpochhammer(c,q,k)/qpochhammer(q,q,k),[p,q],k=0..n);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%'resultG*&*,-%,qpochhammerG6%%\"cG% \"qG,&%\"nG\"\"\"F.F.F.-F(6%%\"aG%\"pGF,F.,&F*!\"\"*&)F2F,F.F1F.F.F.,& F4F.)F+F,F.F.)F*,&F-F4F.F4F.F.**-F(6%F+F+F,F.-F(6%*&*&F1F.F2F.F.F*F4F2 F,F.,&F4F.F1F.F.,&F4F.F*F.F.F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "qsimpcomb(result/qpochhammer(a*p,p,n)/qpochhammer(c*q,q,n)*qp ochhammer(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 "qg osper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^n)^k,q,k,simplify=fal se);" }}{PARA 8 "" 1 "" {TEXT -1 63 "Error, (in qgosper) No q-hypergeo metric 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,simp lify=false);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*,,&!\"\"\"\"\")%\"q G%\"kGF'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'-%,qpochhammerG6%F+F)F*F'F'*&-F66%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(qpoc hhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^10)^k,q,k,simplify=false,solvem ethod=solve): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%Pl! \"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "TIME:=time(): resul t:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^20)^k,q,k,simpli fy=false,solvemethod=solve): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'x!G\"!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q, q,k)/(a*q^10)^k,q,k,simplify=false,solvemethod=gausselim): time()-TIME ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$(o!\"$" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosper(qpochhammer(a,q ,k)/qpochhammer(q,q,k)/(a*q^20)^k,q,k,simplify=false,solvemethod=gauss elim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%cD!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosp er(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^30)^k,q,k,simplify=false ,solvemethod=gausselim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%/x!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=tim e(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^40)^k, q,k,simplify=false,solvemethod=gausselim): time()-TIME;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"&i!>!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpo chhammer(q,q,k)/(a*q^50)^k,q,k,simplify=false,solvemethod=gausselim): \+ time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&x)Q!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosp er(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^60)^k,q,k,simplify=false ,solvemethod=gausselim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&2i(!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=ti me(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^70)^k ,q,k,simplify=false,solvemethod=gausselim): time()-TIME;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"'9k8!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpo chhammer(q,q,k)/(a*q^80)^k,q,k,simplify=false,solvemethod=gausselim): \+ time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'\">5#!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosp er(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^90)^k,q,k,simplify=false ,solvemethod=gausselim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'ERH!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "TIME:=ti me(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^100)^ k,q,k,simplify=false,solvemethod=gausselim): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"']XU!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpo chhammer(q,q,k)/(a*q^10)^k,q,k,simplify=false,solvemethod=ABP): time() -TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$v#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosper(qpochhamme r(a,q,k)/qpochhammer(q,q,k)/(a*q^20)^k,q,k,simplify=false,solvemethod= ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$h*!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosp er(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^30)^k,q,k,simplify=false ,solvemethod=ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" %xI!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): r esult:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^40)^k,q,k,si mplify=false,solvemethod=ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%a*)!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q, k)/(a*q^50)^k,q,k,simplify=false,solvemethod=ABP): time()-TIME;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&#=B!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/ qpochhammer(q,q,k)/(a*q^60)^k,q,k,simplify=false,solvemethod=ABP): tim e()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&nw%!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result:=qgosper(qpoc hhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^70)^k,q,k,simplify=false,solvem ethod=ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&we)!\" $" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=time(): result: =qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^80)^k,q,k,simplify =false,solvemethod=ABP): time()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'ZD;!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "TIME:=ti me(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^90)^k ,q,k,simplify=false,solvemethod=ABP): time()-TIME;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"'Y))>!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "TIME:=time(): result:=qgosper(qpochhammer(a,q,k)/qpochhammer(q, q,k)/(a*q^100)^k,q,k,simplify=false,solvemethod=ABP): time()-TIME;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"''Gv#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "t:=qbrackets(k,p)*qbrackets(k,q)*qbrackets(k,r): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "result:=qsimpcomb(qgosp er(subs(k=k+1,t)-t,[p,q,r],k));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%' resultG*&,0)%\"rG%\"kG\"\"\")%\"qGF)F**&F+F*F'F*!\"\")%\"pGF)F**&F/F*F 'F*F.*&F/F*F+F*F.*(F/F*F+F*F'F*F*F**(,&F0F*F*F.F*,&F,F*F*F.F*,&F(F*F*F .F*F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "qsimpcomb(result-t );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$*(,&%\"pGF$F$!\"\"F$,& %\"qGF$F$F(F$,&%\"rGF$F$F(F$F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 " Section 3" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "qsumrecursion([a,b,q^( -n)],[c,a*b*q^(1-n)/c],q,q,S(n),rec2qhyper=true,sumrange=0..n);" }} {PARA 6 "" 1 "" {TEXT -1 37 "\"Assuming -j to be of type 1-j .. 0.\"" }}{PARA 6 "" 1 "" {TEXT -1 37 "\"Assuming -j to be of type 1-j .. 0.\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$/-%\"SG6#%\"nG*&*&-%,qpochhammer G6%*&%\"cG\"\"\"%\"aG!\"\"%\"qGF(F0-F,6%*&F/F0%\"bGF2F3F(F0F0*&-F,6%F/ F3F(F0-F,6%*&F/F0*&F1F0F7F0F2F3F(F0F21\"\"!F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "term:=_qsumrecursion_proof[_F];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%termG*&**-%,qpochhammerG6%%\"aG%\"qG%\"kG\"\"\" -F(6%%\"bGF+F,F--F(6%)F+,$%\"nG!\"\"F+F,F-)F+F,F-F-*(-F(6%%\"cGF+F,F-- F(6%*&*(F*F-F0F-)F+,&F-F-F5F6F-F-F;F6F+F,F--F(6%F+F+F,F-F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "RE:=_qsumrecursion_proof[_recursion ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#REG/,&*(,&*&)%\"qG%\"nG\"\"\" %\"cGF-F-F+!\"\"F-,&F)F-*(%\"aGF-%\"bGF-F+F-F/F--%\"SG6#F,F-F-*(,&*&F2 F-F+F-F/F)F-F-,&F)F-*&F3F-F+F-F/F--F56#,&F,F-F-F/F-F/\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "cert:=_qsumrecursion_proof[_certifi cate];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%certG,$*&**)%\"qG%\"nG\" \"\",&!\"\"F+)F)%\"kGF+F+,&F)F-*&%\"cGF+F.F+F+F+,&*&F(F+F2F+F+*(%\"aGF +%\"bGF+F)F+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\},lhs(RE))-(sub s(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): sum2qhyp er(term,q,k); n:='n':" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*&**-%,qpochh ammerG6%%\"qGF(,&%#n|irG\"\"\"%\"bGF+F+-F&6%F(F(,&F*F+%\"cGF+F+-F&6%F( F(,&F,F+F0F+F+-%$phiG6&7&)F(,$F,!\"\")F(,$F*F:)F(,$F0F:F(7%)F(,&F+F+F* F+)F(,&F+F+F0F+)F(,&F+F+F,F+F(**F(F+)F(F,F+)F(F*F+)F(F0F+F+F+*()-F&6%F (F(F*\"\"#F+)-F&6%F(F(F,FNF+)-F&6%F(F(F0FNF+F:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 40 "qDixon_RE:=qsumrecursion(term,q,k,S(n));" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%*qDixon_REG/,**,)%\"qG\"\"$\"\"\",&) F)%\"nGF+F+!\"\"F+,&F-F+F+F+F+,&)F),$F.\"\"#F+F)F/F+-%\"SG6#F.F+F+*(F) F+,J)F),*F.\"\"%F+F+%\"cGF+%\"bGF+F+)F),(F.FF+F=F+F+)F),*F4F+*&FF+F+)F),*F.F4F>F+F=F+F4F+F/)F),*F*F+F.F+F=F+F>F+F/)F),*FF+F/)F),(F4F+*&F*F+F.F+F+F>F+F/)F),(F.F4F>F+F*F+F+)F),(F.F4 F>F+F4F+F+)F),(F*F+F.F+F>F+F/)F),(F4F+*&F*F+F.F+F+F=F+F/)F),(F.F4F=F+F *F+F+)F),(F.F4F=F+F4F+F+)F),(F*F+F.F+F=F+F/)F),&F4F+*&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(F+F+*$)F)F F+F=F+F+F)F/F+,B*$)F)\"\"'F+F /)F),(F.F*F>F+F=F+F+F_oF/)F),(FF+F+FQF+FcoF/FMF/)F),*F+F+*&F* F+F.F+F+F>F+F=F+F+)F),&F.F4F4F+F/)F),*F4F+*&F*F+F.F+F+F=F+F>F+F+FHF+FO F/FXF/FZF+FVF/)F),(FF+F+F+,&FjoF+FcqF/F+,&FcqF/)F),&F.F+F=F+F+F+-F66#,&F.F+ F*F/F+F/\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "M:=qsimpco mb(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#/,&*&,&\"\" \"F')%\"qG%\"nG!\"\"F'-%\"SG6#F*F'F'*&,&F+F')F),(F*F'%\"bGF'%\"cGF'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 "TIME:=time():\nleftRE:=qsumrecursion(qpochhammer(a,q ,k)*qpochhammer(a*q^2,q^2,k)*qpochhammer(b,q,k)*qpochhammer(c,q,k)*qpo chhammer(d,q,k)*qpochhammer(e,q,k)*qpochhammer(q^(-n),q,k)*(a^2*q^(2+n )/(b*c*d*e))^k/(qpochhammer(a,q^2,k)*qpochhammer(a/b*q,q,k)*qpochhamme r(a/c*q,q,k)*qpochhammer(a/d*q,q,k)*qpochhammer(a/e*q,q,k)*qpochhammer (a*q^(n+1),q,k)*qpochhammer(q,q,k)),q,k,S(n));\ntime()-TIME;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'leftREG/,(*.%\"qG\"\"\",&*&)F(%\"nGF)%\"a GF)F)%\"cG!\"\"F),&F+F)%\"dGF0F),&F+F)%\"eGF0F),&F+F)%\"bGF0F)-%\"SG6# F-F)F)*(,&F0F)F+F)F),B*&)F(,&F-\"\"$F)F)F))F.F@F)F)*,F(F)F6F)F/F)F2F)F 4F)F0*,)F(\"\"#F)F6F)F/F)F2F)F4F)F0*&)F(,&FEF)F-F)F))F.FEF)F)*.F6F))F( ,$F-FEF)F4F)F.F)F/F)F2F)F0*&)F(,$F-F@F)FAF)F)*,F6F))F(,&F-F)F)F)F)F.F) F/F)F2F)F)*,FQF)F4F)F.F)F/F)F2F)F)*,F6F)FQF)F4F)F/F)F2F)F)*()F(,&F-FEF )F)F)F4F)FIF)F0*(FVF)FIF)F/F)F0*(FVF)FIF)F2F)F0*,F6F)FQF)F4F)F.F)F2F)F )*,F6F)FQF)F4F)F.F)F/F)F)*(F6F)FVF)FIF)F0*&FVF)FAF)F0F)-F86#,&F-F)F)F0 F)F0*,,&**F6F)F/F)F2F)F4F)F0*&FIF)F,F)F)F)F;F),&F,F)F(F0F),&F(F0F+F)F) -F86#,&F-F)FEF0F)F)\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$q)!\"$ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 344 "TIME:=time():\nrightRE :=qsumrecursion(qpochhammer(a/(b*c)*q,q,k)*qpochhammer(d,q,k)*qpochham mer(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)*qpochh ammer(d*e/a*q^(-n),q,k)*qpochhammer(q,q,k)*qpochhammer(a/d*q,q,n)*qpoc hhammer(a/e*q,q,n)),q,k,S(n));\ntime()-TIME;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(rightREG/,(*.%\"qG\"\"\",&*&)F(%\"nGF)%\"aGF)F)%\"cG !\"\"F),&F+F)%\"dGF0F),&F+F)%\"eGF0F),&F+F)%\"bGF0F)-%\"SG6#F-F)F)*(,& F0F)F+F)F),B*&)F(,&F-\"\"$F)F)F))F.F@F)F)*,F(F)F6F)F/F)F2F)F4F)F0*,)F( \"\"#F)F6F)F/F)F2F)F4F)F0*&)F(,&FEF)F-F)F))F.FEF)F)*.F6F))F(,$F-FEF)F4 F)F.F)F/F)F2F)F0*&)F(,$F-F@F)FAF)F)*,F6F))F(,&F-F)F)F)F)F.F)F/F)F2F)F) *,FQF)F4F)F.F)F/F)F2F)F)*,F6F)FQF)F4F)F/F)F2F)F)*()F(,&F-FEF)F)F)F4F)F IF)F0*(FVF)FIF)F/F)F0*(FVF)FIF)F2F)F0*,F6F)FQF)F4F)F.F)F2F)F)*,F6F)FQF )F4F)F.F)F/F)F)*(F6F)FVF)FIF)F0*&FVF)FAF)F0F)-F86#,&F-F)F)F0F)F0*,,&** F6F)F/F)F2F)F4F)F0*&FIF)F,F)F)F)F;F),&F,F)F(F0F),&F(F0F+F)F)-F86#,&F-F )FEF0F)F)\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$q%!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "`recursion/compare`(leftRE,r ightRE,S(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Recursions~are~iden tical.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:=q sumrecursion(qpochhammer(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)*qpochhammer(q,q,k)),q,k,S(n)):\ntime()-TIME;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"%bR!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 590 "c:=a^2*q/(b*d*lam):\nTIME:=time():\nrightRE:=qsumrec ursion(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)*qpochham mer(lam*q^2,q^2,k)*qpochhammer(b*lam/a,q,k)*qpochhammer(c*lam/a,q,k)*q pochhammer(d*lam/a,q,k)*qpochhammer(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)*qpochhamme r(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)*qpochhammer(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#$\"&NE\"!\"$" }}}{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.28)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 499 "c:=a^2*q /(b*d*lam):\nTIME:=time():\nleftRE:=qsumrecursion(qpochhammer(a,q,k)*q pochhammer(a*q^2,q^2,k)*qpochhammer(b,q,k)*qpochhammer(c,q,k)*qpochham mer(d,q,k)*qpochhammer(e,q,k)*qpochhammer(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)*qpoc hhammer(a/b*q,q,k)*qpochhammer(a/c*q,q,k)*qpochhammer(a/d*q,q,k)*qpoch hammer(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)*qpochhammer(q,q,k)),q,k,S(n)):\ntime()-T IME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&7r\"!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 732 "c:=a^2*q/(b*d*lam):\nTIME:=time():\nrigh tRE:=qsumrecursion(qpochhammer(lam,q,k)*qpochhammer(lam*q^2,q^2,k)*qpo chhammer(b*lam/a,q,k)*qpochhammer(c*lam/a,q,k)*qpochhammer(d*lam/a,q,k )*qpochhammer(e,q,k)*qpochhammer(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)/(qpochh ammer(lam,q^2,k)*qpochhammer(a/b*q,q,k)*qpochhammer(a/c*q,q,k)*qpochha mmer(a/d*q,q,k)*qpochhammer(lam/e*q,q,k)*qpochhammer(lam/f*q,q,k)*qpoc hhammer(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,r ightRE,S(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Recursions~are~iden tical.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 "qsumrecursion([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)*(,&)F',$F(\"\"#F+F'F)F),,*&F'F)%\"xGF)F)*&)F ',&F(F)F)F)F)F7F)F)*&F4F)F&F)F+*&F7F)F&F)F)*&F2F)F7F)F)F)-F.6#,&F(F)F) F+F)F+**,&F&F)F)F)F),&F'F)F&F+F)F&F)-F.6#,&F(F)F4F+F)F+\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "qsumrecursion([q^(-n),q^(n+1 )],[q],q,q*q^y,p(y));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/,(*()%\"qG,& %\"nG\"\"\"F*F*F*,&!\"\"F*)F'%\"yGF*F*-%\"pG6#F.F*F**&,()F',(F.F**&\" \"#F*F)F*F*F*F*F,F-F,*&F7F*F&F*F*F*-F06#,&F.F*F*F,F*F**(,&F-F*F'F,F*)F 'F)F*-F06#,&F.F*F7F,F*F*\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "qsumdiffeq([q^(-n),q^(n+1)],[q],q,q*x,p(x));" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#/,(**,&)%\"qG%\"nG\"\"\"F*!\"\"F*,&*&F'F*F(F*F*F*F+F* F(F*-%\"pG6#%\"xGF*F**(,&F+F*F(F*F*,.*()F(\"\"#F*F1F*)F'F7F*F*F'F+*&F( F*F1F*F*F-F**()F(\"\"$F*F1F*F'F*F+*(F6F*F1F*F'F*F+F*-&%#DqGF06#F.F*F** .F'F*,&F+F**&F6F*F1F*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),rec2qhyper=true);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7 $/-%\"pG6#%\"nG*&),$%\"qG!\"\"F(\"\"\")F,-%)binomialG6$F(\"\"#F.1\"\"! F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Al-Salam-Chihara polynomial s" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "re1:= qsumrecursion(qpochhamm er(a*b,q,n)/a^n,\n[q^(-n),a*exp(I*theta),a*exp(-I*theta)],[a*b,0],q,q, Q(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$re1G/,(*()%\"qG\"\"$\"\" \"-%$expG6#*&^#F+F+%&thetaGF+F+-%\"QG6#%\"nGF+F+*(,**(F,F+)F)F5F+%\"aG F+F+F)!\"\"*(F,F+F9F+%\"bGF+F+*&F)F+)F,\"\"#F+F;F+)F)F@F+-F36#,&F5F+F+ F;F+F+**F,F+,&*$FAF+F;*(F:F+F=F+F9F+F+F+,&F9F+F)F;F+-F36#,&F5F+F@F;F+F +\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "re2:= qsumrecurs ion(qpochhammer(b*exp(-I*theta),q,n)*exp(I*n*theta),\n[q^(-n),a*exp(I* theta)],[b^(-1)*q^(1-n)*exp(I*theta)],\nq,b^(-1)*q*exp(-I*theta),Q(n)) ;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$re2G/,(*(-%$expG6#*&%\"IG\"\" \"%&thetaGF-F-)%\"qG\"\"$F--%\"QG6#%\"nGF-!\"\"*(,**(F(F-)F0F5F-%\"aGF -F-F0F6*(F(F-F:F-%\"bGF-F-*&F0F-)F(\"\"#F-F6F-)F0F@F--F36#,&F5F-F6F-F- F6**F(F-,&*$FAF-F6*(F;F-F=F-F:F-F-F-,&F:F6F0F-F--F36#,&F5F-!\"#F-F-F- \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "`recursion/compare `(re1,re2,Q(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Recursions~are~i dentical.G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Askey-Wilson polyno mials" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 362 "c:= (k,n,a,b,c,d,alpha,be ta,gamma,j) ->\nqpochhammer(alpha*d,beta*d,gamma*d,q,q,n)*qpochhammer( alpha*beta*gamma*d*q^(n-1),q,k)/qpochhammer(alpha*d,beta*d,gamma*d,q,a *b*c*d*q^(k-1),q,k)/qpochhammer(q,q,n-k)*q^(k^2-n*k)*d^(k-n)*qphihyper term([q^(k-n),alpha*beta*gamma*d*q^(n+k-1),a*d*q^k,b*d*q^k,c*d*q^k],[a *b*c*d*q^(2*k),alpha*d*q^k,beta*d*q^k,gamma*d*q^k],q,q,j);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"cGR6,%\"kG%\"nG%\"aG%\"bGF$%\"dG%&alphaG %%betaG%&gammaG%\"jG6\"6$%)operatorG%&arrowGF0*&*,-%,qpochhammerG6(*&9 *\"\"\"9)F;*&9+F;FF;F@F;FF;F@F;FF;F " 0 "" {MPLTEXT 1 0 139 "intermediate:=qsumre cursion(c(k,N+k,a,b,c,d,alpha,b,c,j),q,j,S(N),rec2qhyper=true,sumrange =0..N):\nfinal:= subs(N=n-k,rhs(intermediate[1]));" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%&finalG*&*6,&%\"qG!\"\"*,%&alphaG\"\"\"%\"dGF,)F(% \"kGF,%\"cGF,%\"bGF,F,F,-%,qpochhammerG6%F*F(F/F,,&F(F)*,%\"aGF,F1F,F0 F,F-F,)F.\"\"#F,F,F,-F36%*(F1F,F0F,F.F,F(,&%\"nGF,F/F)F,-F36%*&*,F+F,F 1F,F0F,F-F,F8F,F,F(F)F(F=F,-F36%*&F+F,F7F)F(F=F,-F36%*&F(F,F.F,F(F=F,- F36%*(F0F,F-F,F.F,F(F=F,-F36%*(F1F,F-F,F.F,F(F=F,)F7F=F,F,*.,&F(F)*,F+ F,F1F,F0F,F-F,F8F,F,F,,&F(F)*,F7F,F1F,F0F,F-F,F.F,F,F,-F36%FTF(F/F,-F3 6%F(F(F=F,-F36%F6F(F=F,-F36%*&*,F+F,F-F,F.F,F0F,F1F,F,F(F)F(F=F,F)" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 228 "RHS:=qpochhammer(alpha/a,q ,n-k)*qpochhammer(alpha*b*c*d*q^(n-1),q,k)*qpochhammer(b*c,b*d,c*d,q,n )*a^(n-k)*qpochhammer(q,q,n)/(qpochhammer(q,b*c,b*d,c*d,q,k)*qpochhamm er(a*b*c*d*q^(k-1),q,k)*qpochhammer(q,a*b*c*d*q^(2*k),q,n-k));" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%$RHSG*&*0-%,qpochhammerG6%*&%&alphaG \"\"\"%\"aG!\"\"%\"qG,&%\"nGF,%\"kGF.F,-F(6%*,F+F,%\"bGF,%\"cGF,%\"dGF ,)F/,&F1F,F.F,F,F/F2F,-F(6%*&F6F,F7F,F/F1F,-F(6%*&F6F,F8F,F/F1F,-F(6%* &F7F,F8F,F/F1F,)F-F0F,-F(6%F/F/F1F,F,*0-F(6%F/F/F2F,-F(6%F=F/F2F,-F(6% F@F/F2F,-F(6%FCF/F2F,-F(6%*,F-F,F6F,F7F,F8F,)F/,&F2F,F.F,F,F/F2F,-F(6% F/F/F0F,-F(6%*,F-F,F6F,F7F,F8F,)F/,$F2\"\"#F,F/F0F,F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "qsimpcomb(final/RHS);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "RE2:=qsumrecursion(c(k,N+k,a,b,c,d,a,beta,c,j),q,j,S(N),rec2qhy per=true):\nfinal2:= subs(N=n-k,rhs(RE2[1]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'final2G*&*6,&%\"qG!\"\"*,%\"aG\"\"\"%%betaGF,%\"dGF, )F(%\"kGF,%\"cGF,F,F,-%,qpochhammerG6%F*F(F0F,,&F(F)*,F+F,%\"bGF,F1F,F .F,)F/\"\"#F,F,F,-F36%*(F+F,F1F,F/F,F(,&%\"nGF,F0F)F,-F36%*&*,F+F,F-F, F.F,F8F,F1F,F,F(F)F(F=F,-F36%*&F-F,F7F)F(F=F,-F36%*&F(F,F/F,F(F=F,-F36 %*(F1F,F.F,F/F,F(F=F,-F36%*(F+F,F.F,F/F,F(F=F,)F7F=F,F,*.,&F(F)*,F+F,F -F,F.F,F8F,F1F,F,F,,&F(F)*,F+F,F7F,F1F,F.F,F/F,F,F,-F36%FTF(F0F,-F36%F (F(F=F,-F36%F6F(F=F,-F36%*&*,F+F,F-F,F.F,F/F,F1F,F,F(F)F(F=F,F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "RE3:=qsumrecursion(c(k,N+k, a,b,c,d,a,b,gamma,j),q,j,S(N),rec2qhyper=true):\nfinal3:= subs(N=n-k,r hs(RE3[1]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'final3G*&*6,&%\"qG! \"\"*,%\"aG\"\"\"%\"dGF,)F(%\"kGF,%&gammaGF,%\"bGF,F,F,-%,qpochhammerG 6%F*F(F/F,,&F(F)*,F+F,F1F,%\"cGF,F-F,)F.\"\"#F,F,F,-F36%*&F0F,F7F)F(,& %\"nGF,F/F)F,-F36%*(F+F,F1F,F.F,F(F=F,-F36%*&*,F+F,F1F,F0F,F-F,F8F,F,F (F)F(F=F,-F36%*&F(F,F.F,F(F=F,-F36%*(F1F,F-F,F.F,F(F=F,-F36%*(F+F,F-F, F.F,F(F=F,)F7F=F,F,*.,&F(F)*,F+F,F1F,F0F,F-F,F8F,F,F,,&F(F)*,F+F,F1F,F 7F,F-F,F.F,F,F,-F36%FTF(F/F,-F36%F(F(F=F,-F36%F6F(F=F,-F36%*&*,F+F,F-F ,F.F,F0F,F1F,F,F(F)F(F=F,F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Sec tion 4" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "TIME:=time(): Sn:=qrecsol ve(qDixon_RE,q,S(n),output=qhypergeometric);\ntime()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#SnG7#7$*&-%,qpochhammerG6%)%\"qG,(%\"cG\" \"\"F/F/%\"bGF/F,%\"nGF/-F)6%F,F,F1!\"\"1\"\"!F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&g)f!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "TIME:=time(): Sn:=qrecsolve(qDixon_RE,q,S(n),output=qhypergeometri c,split=false);\ntime()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Sn G7#7$*&-%,qpochhammerG6%)%\"qG,(%\"bG\"\"\"%\"cGF/F/F/F,%\"nGF/-F)6%F, F,F1!\"\"1\"\"!F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&S5#!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "qsimplify(Sn[1][1]*qpochham mer(q,q,n)*qpochhammer(q,q,b)*qpochhammer(q,q,c)/qpochhammer(q,q,n+b+c ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*&-%,qpochhammerG6%%\"qGF(%\" cG\"\"\",&!\"\"F*)F(%\"bGF*F*F**&,&F,F**&)F(F)F*F-F*F*F*-F&6%F-F(F)F*F ," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 191 "qrecsolve(q^k*(q+1)*( q-1)*(q^(k+1)-1)*F(k+2)+(q+1)*(1-q^(k+1))*(q^k*(a*q-a)+a-1)*F(k+1)+(a+ 1)*(a-1)*(q^(k+1)-1)*F(k)=(a-1)*(a-q)*(q^k+1)*(q^k-1)*qpochhammer(a,q, k)/qpochhammer(q,q,k),q,F(k));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#,$ *&*&,&)%\"qG%\"kG\"\"\"!\"\"F+F+-%,qpochhammerG6%%\"aGF)F*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=seri es);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#-%$SumG6$*&*(%$_C1G\"\"\")% \"qG*$)%#_iG\"\"#F*F*))F,%\"nGF/F*F*-%,qpochhammerG6%F,F,F/!\"\"/F/;\" \"!%)infinityG" }}}{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\"\"\"-%,qpo chhammerG6%)F*,$%\"nG!\"\"F*F+F,))F*%\"kGF+F,F,*&-F.6%*&F0F,%\"aGF3F*F +F,,&*&F;F,)F*F2F,F,F)F3F,F3/F+;\"\"!%)infinityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "assume(n,posint);\nqgosper(qpochhammer(a,q,k) /qpochhammer(q,q,k)/(a*q^n)^k,q,k,series=true);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*&*.,&)%\"qG%\"kG\"\"\"!\"\"F)F)%\"aGF))F'%#n|irGF)-%$S umG6$*&*&-%,qpochhammerG6%)F',$F-F*F'%#_iGF))F'*&F(F)F8F)F)F)*&-F46%*& F6F)F+F*F'F8F),&*&F+F)F,F)F))F'F8F*F)F*/F8;\"\"!F-F)-F46%F+F'F(F))F@,$ F(F*F)F)-F46%F'F'F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }