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{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 25 "restart; read `qsum.mpl`;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#%OCopyright~1998,~~Harald~Boeing~&~Wo
lfram~KoepfG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%;Konrad-Zuse-Zentrum~
BerlinG" }}}{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*qpoc
hhammer(a,p,k)/qpochhammer(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.)F+F,F.F.,&F*F4*&F1F.)F2F,F.F.F.)F*,&F-F4F4F.F.\"\"\"**-F(6%F+F+F,
\"\"\"-F(6%*&*&F1F;F2F.F;F*!\"\"F2F,\"\"\",&F4F.F1F.\"\"\",&F4F.F*F.\"
\"\"FD" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "qsimpcomb(result
/qpochhammer(a*p,p,n)/qpochhammer(c*q,q,n)*qpochhammer(a*p/c,p,n)*qpoc
hhammer(q,q,n)*c^n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "qgosper(qpochhammer(a,q,k)/q
pochhammer(q,q,k)/(a*q^n)^k,q,k,simplify=false);" }}{PARA 8 "" 1 "" 
{TEXT -1 62 "Error, (in qgosper) No q-hypergeometric antidifference ex
ists." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "qgosper(qpochhamme
r(a,q,k)/qpochhammer(q,q,k)/(a*q)^k,q,k,simplify=false);" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#*&*,,&!\"\"\"\"\")%\"qG%\"kGF'F'%\"aG\"\"\"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)\"\"\"F1F'F'-%,qpochhammerG6%F+F)F*F'F,*&-F;6%F)F)F*\"
\"\")F0F*\"\"\"F1" }}}{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#!\"$" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 48 "t:=qbrackets(k,p)*qbrackets(k,q)*qbrackets(k,r):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "result:=qsimpcomb(qgosp
er(subs(k=k+1,t)-t,[p,q,r],k));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'
resultG*&,0)%\"rG%\"kG\"\"\")%\"qGF)F**&F+F*F'F*!\"\")%\"pGF)F**&F/F*F
'\"\"\"F.*&F/F2F+F2F.*(F/F2F+F2F'F2F*F2*(,&F0F*F.F*\"\"\",&F,F*F.F*\"
\"\",&F(F*F.F*\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
20 "qsimpcomb(result-t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$
*(,&%\"pG\"\"\"!\"\"F(\"\"\",&%\"qGF(F)F(\"\"\",&%\"rGF(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 12 "" 1 "" {XPPMATH 20 "6
#7$/-%\"SG6#%\"nG*&*&-%,qpochhammerG6%*&%\"cG\"\"\"%\"aG!\"\"%\"qGF(\"
\"\"-F,6%*&F/F0%\"bGF2F3F(F4F0*&-F,6%*&F/F0*&F1\"\"\"F8\"\"\"F2F3F(\"
\"\"-F,6%F/F3F(\"\"\"F21\"\"!F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 31 "term:=_qsumrecursion_proof[_F];" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#>%%termG*&**-%,qpochhammerG6%%\"aG%\"qG%\"kG\"\"\"-F(6%%\"bGF+F,
F--F(6%)F+,$%\"nG!\"\"F+F,F-)F+F,F-\"\"\"*(-F(6%%\"cGF+F,\"\"\"-F(6%*&
*(F*F-F0F-)F+,&F-F-F5F6F-F8F<!\"\"F+F,\"\"\"-F(6%F+F+F,\"\"\"FD" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "RE:=_qsumrecursion_proof[_re
cursion];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#REG/,&*(,&*&)%\"qG%\"n
G\"\"\"%\"cGF-!\"\"*&%\"aGF-F+F-F-F-,&*&%\"bGF-F+\"\"\"F-F)F/F--%\"SG6
#,&F,F-F/F-F-F-*(,&F)F/*(F1F5F4F5F+F5F-F-,&F)F/F+F-F--F76#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(F-*&%\"cGF-F.F-F,F-,&*&F'F-F
2F*F,*(%\"aGF-%\"bGF-F(F-F-F-F**&,&F'F-F,F-\"\"\"F.\"\"\"!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "i:=_qsumrecursion_proof[_sum
var];" }}{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))-(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#*&**)!\"\"%#n|irG\"\"\")%\"qG,&*$)F'\"\"#\"\"\"#\"\"
$F.F'#F(F.F(-%,qpochhammerG6%F*F*,&%\"bGF(%\"cGF(F(-%$phiG6&7%)F*,&F8F
&F'F&)F*,$F'!\"#)F*,&F7F&F'F&7$)F*,(F(F(F8F(F'F&)F*,(F(F(F7F(F'F&F*)F*
,*F(F(F7F(F'F(F8F(F(F/*(-F46%F*F*,&F8F(F'F&\"\"\"-F46%F*F*,$F'F.\"\"\"
-F46%F*F*,&F7F(F'F&\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 40 "qDixon_RE:=qsumrecursion(term,q,k,S(n));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%*qDixon_REG/,**,,&)%\"qG,$%\"nG\"\"#!\"\"F*\"\"\"F/,&
)F*F,F/F/F/F/)F*\"\"$\"\"\",&F1F/F.F/F/-%\"SG6#F,F/F/*(,J)F*,*\"\"%F/F
,F/%\"cGF/%\"bGF/F/)F*,(F,F-F?F/F3F/F.)F*,*F3F/F,F/F>F/F?F/F/)F*,(F3F/
F,F/F?F/F/)F*,*F,F=F-F/F>F/F?F/F.)F*,(F,F3F-F/F?F/F/)F*,*F,F-F?F/F>F/F
-F/F/)F*,(F,F-F?F/F-F/F.)F*,*F/F/F,F=F?F/F>F/F.)F*,(F,F=F?F/F>F/F.*$)F
*\"\"&F4F.*$)F*F=F4F.)F*,&F3F/F,F-F/)F*,(F,F-F>F/F3F/F.)F*,(F3F/F,F/F>
F/F/*$F2F4F.)F*,(F,F3F-F/F>F/F/)F*,&F,F3F-F/F/)F*,(F,F-F>F/F-F/F.)F*,&
F,F3F/F/F/F/F*F/-F76#,&F,F/F.F/F/F.*(,B)F*,(F=F/F,F/F?F/F/FRF.*$)F*\"
\"'F4F.)F*,(F,F3F>F/F?F/F/)F*,&F,F-F-F/F.)F*,*F,F3F-F/F>F/F?F/F/FLF.F;
F/FUF.)F*,*F,F3F/F/F?F/F>F/F/FDF/F@F.F\\oF.FenF/FYF.)F*,(F=F/F,F/F>F/F
/F/,&F*F.)F*,(F,F/F?F/F>F/F/F/-F76#,&F,F/!\"#F/F/F.*,,&*$)F*F-F4F.)F*,
&F,F/F?F/F/F/,&F]qF/)F*,&F,F/F>F/F.F/,&FepF/F]qF.F/FdpF4-F76#,&F,F/!\"
$F/F/F.\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "M:=qsimpcom
b(subs(k=-k,term)/term);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG)%\"
qG%\"kG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "qsumrecursion((1
+M)/2*term,q,k,S(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&,&\"\"\"
F')%\"qG%\"nG!\"\"F'-%\"SG6#F*F'F'*&,&)F),(F*F'%\"bGF'%\"cGF'F'F+F'F'-
F-6#,&F*F'F+F'F'F'\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Table 2
" }}{PARA 0 "" 0 "" {TEXT -1 8 "(III.18)" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 390 "TIME:=time():\nleftRE:=qsumrecursion(qpochhammer(a,q
,k)*qpochhammer(a*q^2,q^2,k)*qpochhammer(b,q,k)*qpochhammer(c,q,k)*qpo
chhammer(d,q,k)*qpochhammer(e,q,k)*qpochhammer(q^(-n),q,k)*(a^2*q^(2+n
)/(b*c*d*e))^k/(qpochhammer(a,q^2,k)*qpochhammer(a/b*q,q,k)*qpochhamme
r(a/c*q,q,k)*qpochhammer(a/d*q,q,k)*qpochhammer(a/e*q,q,k)*qpochhammer
(a*q^(n+1),q,k)*qpochhammer(q,q,k)),q,k,S(n));\ntime()-TIME;" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%'leftREG/,(*.%\"qG\"\"\",&*&)F(%\"nGF)%\"a
GF)F)%\"cG!\"\"F),&F+F)%\"dGF0F),&F+F0%\"eGF)F),&F+F0%\"bGF)F)-%\"SG6#
F-F)F0*(,&F0F)F+F)F),B*,F2F))F(,&F-F)F)F)F)F4F)F.\"\"\"F/F)F)*,F2F@F6F
)F>F@F4F@F.F@F)*,F6F@F>F@F4F@F.F@F/F@F)*()F(,&F-\"\"#F)F)F))F.FFF@F/F@
F0*,F2F@F6F@F>F@F4F@F/F@F)*(FDF@F4F@FGF@F0*(F2F@FDF@FGF@F0*(F6F@FDF@FG
F@F0*,F2F@F6F@F>F@F.F@F/F@F)*&FDF@)F.\"\"$F@F0*,)F(FFF@F6F@F/F@F2F@F4F
@F0*&)F(,&FFF)F-F)F)FGF@F)*.F2F@F6F@)F(,$F-FFF)F4F@F.F@F/F@F0*&)F(,$F-
FOF)FNF@F)*&)F(,&F-FOF)F)F)FNF@F)*,F(F@F6F@F/F@F2F@F4F@F0F)-F86#,&F-F)
F0F)F)F)*,,&**F6F@F/F@F2F@F4F@F)*&FGF@F,F@F0F)F;F@,&F,F0F(F)F),&F(F0F+
F)F)-F86#,&F-F)!\"#F)F)F0\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%
y>!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 344 "TIME:=time():\nr
ightRE:=qsumrecursion(qpochhammer(a/(b*c)*q,q,k)*qpochhammer(d,q,k)*qp
ochhammer(e,q,k)*qpochhammer(q^(-n),q,k)*qpochhammer(a*q,q,n)*qpochham
mer(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)%\"
cG!\"\"F),&F+F)%\"dGF0F),&F+F0%\"eGF)F),&F+F0%\"bGF)F)-%\"SG6#F-F)F0*(
,&F0F)F+F)F),B*,F2F))F(,&F-F)F)F)F)F4F)F.\"\"\"F/F)F)*,F2F@F6F)F>F@F4F
@F.F@F)*,F6F@F>F@F4F@F.F@F/F@F)*()F(,&F-\"\"#F)F)F))F.FFF@F/F@F0*,F2F@
F6F@F>F@F4F@F/F@F)*(FDF@F4F@FGF@F0*(F2F@FDF@FGF@F0*(F6F@FDF@FGF@F0*,F2
F@F6F@F>F@F.F@F/F@F)*&FDF@)F.\"\"$F@F0*,)F(FFF@F6F@F/F@F2F@F4F@F0*&)F(
,&FFF)F-F)F)FGF@F)*.F2F@F6F@)F(,$F-FFF)F4F@F.F@F/F@F0*&)F(,$F-FOF)FNF@
F)*&)F(,&F-FOF)F)F)FNF@F)*,F(F@F6F@F/F@F2F@F4F@F0F)-F86#,&F-F)F0F)F)F)
*,,&**F6F@F/F@F2F@F4F@F)*&FGF@F,F@F0F)F;F@,&F,F0F(F)F),&F(F0F+F)F)-F86
#,&F-F)!\"#F)F)F0\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%n6!\"$" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "`recursion/compare`(leftR
E,rightRE,S(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Recursions~are~i
dentical.G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "(III.25)" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 307 "c:=a^2*q/(b*d*lam):\nTIME:=time():\nleftRE
:=qsumrecursion(qpochhammer(a,q,k)*qpochhammer(b,q,k)*qpochhammer(c,q,
k)*qpochhammer(d,q,k)*qpochhammer(q^(-n),q,k)*q^k/(qpochhammer(a/b*q,q
,k)*qpochhammer(a/c*q,q,k)*qpochhammer(a/d*q,q,k)*qpochhammer(a^2/lam^
2*q^(-n),q,k)*qpochhammer(q,q,k)),q,k,S(n)):\ntime()-TIME;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"%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),,*&F2F)%\"xGF)F)*&F7
\"\"\"F&F9F)F&!\"#*&)F',&F(F)F)F)F)F7F9F)*&F'F)F7F9F)F)-F.6#,&F(F)F+F)
F)F)**,&F&F)F)F)F),&F&F)F'F+F)F&F9-F.6#,&F(F)F:F)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%\"yG\"
\"\"!\"\"F*F*)F(,&%\"nGF*F*F*F*-%\"pG6#F)F*F**&,(F'F+)F(,(F)F*F.\"\"#F
*F*F+F,F6F*-F06#,&F)F*F+F*F*F**(,&F'F+F(F*F*)F(F.F*-F06#,&F)F*!\"#F*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&%\"nG\"\"\"!\"\"F+F+,&*&F)F+F&F+F+F,F+F+-%\"pG6#%\"xGF+
F+*(,&F,F+F&F+F+,.*()F&\"\"$F'F2F+F)F'F+*()F&\"\"#F'F2F')F)F;F'F,*(F:F
'F2F'F)F'F+F.F,*&F&F'F2F'F,F)F+F+-&%#DqGF16#F/F+F,*.F2F'F)F')F4F;F',&*
&F:F'F2F'F+F,F+F+F&F'-&FA6$F2F2FBF+F,\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 61 "qsumrecursion([q^(-n),q^(n+1)],[q],q,q,p(n),rec2qhy
per=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/,(*(-%$expG6#*&%\"IG\"\"\"%&thetaGF-F-)%\"
qG\"\"$\"\"\"-%\"QG6#%\"nGF-!\"\"*(,**(F(F2)F0F6F-%\"aGF-F-F0F7*(F(F2F
;F2%\"bGF-F-*&F0F-)F(\"\"#F2F7F-)F0FAF2-F46#,&F6F-F7F-F-F7**F(F2,&*$FB
F2F7*(F<F2F>F2F;F2F-F-,&F;F7F0F-F--F46#,&F6F-!\"#F-F-F-\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "re2:= qsumrecursion(qpochha
mmer(b*exp(-I*theta),q,n)*exp(I*n*theta),\n[q^(-n),a*exp(I*theta)],[b^
(-1)*q^(1-n)*exp(I*theta)],\nq,b^(-1)*q*exp(-I*theta),Q(n));" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%$re2G/,(*(-%$expG6#*&%\"IG\"\"\"%&thetaGF-
F-)%\"qG\"\"$\"\"\"-%\"QG6#%\"nGF-!\"\"*(,**(F(F2)F0F6F-%\"aGF-F-F0F7*
(F(F2F;F2%\"bGF-F-*&F0F-)F(\"\"#F2F7F-)F0FAF2-F46#,&F6F-F7F-F-F7**F(F2
,&*$FBF2F7*(F<F2F>F2F;F2F-F-,&F;F7F0F-F--F46#,&F6F-!\"#F-F-F-\"\"!" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "`recursion/compare`(re1,re2
,Q(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Recursions~are~identical.
G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Askey-Wilson polynomials" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 362 "c:= (k,n,a,b,c,d,alpha,beta,gamma,
j) ->\nqpochhammer(alpha*d,beta*d,gamma*d,q,q,n)*qpochhammer(alpha*bet
a*gamma*d*q^(n-1),q,k)/qpochhammer(alpha*d,beta*d,gamma*d,q,a*b*c*d*q^
(k-1),q,k)/qpochhammer(q,q,n-k)*q^(k^2-n*k)*d^(k-n)*qphihyperterm([q^(
k-n),alpha*beta*gamma*d*q^(n+k-1),a*d*q^k,b*d*q^k,c*d*q^k],[a*b*c*d*q^
(2*k),alpha*d*q^k,beta*d*q^k,gamma*d*q^k],q,q,j);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%\"cGR6,%\"kG%\"nG%\"aG%\"bGF$%\"dG%&alphaG%%betaG%&ga
mmaG%\"jG6\"6$%)operatorG%&arrowGF0*&*,-%,qpochhammerG6(*&9*\"\"\"9)F;
*&9+F;F<\"\"\"*&9,F;F<F?%\"qGFB9%F;-F76%*,F:F?F>F?FAF?F<F?)FB,&FCF;!\"
\"F;F;FB9$F;)FB,&*$)FJ\"\"#F?F;*&FCF;FJF;FIF;)F<,&FJF;FCFIF;-%.qphihyp
ertermG6'7')FBFR*,F:F?F>F?FAF?F<F?)FB,(FCF;FJF;FIF;F;*(9&F?F<F?)FBFJF;
*(9'F?F<F?FgnF?*(9(F?F<F?FgnF?7&*,FfnF?FinF?F[oF?F<F?)FB,$FJFOF;*(F:F?
F<F?FgnF?*(F>F?F<F?FgnF?*(FAF?F<F?FgnF?FBFB9-F;F?*&-F76)F9F=F@FB*,FfnF
;FinF;F[oF;F<F?)FB,&FJF;FIF;F;FBFJ\"\"\"-F76%FBFB,&FCF;FJFI\"\"\"!\"\"
F0F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "intermediate:=qs
umrecursion(c(k,N+k,a,b,c,d,alpha,b,c,j),q,j,S(N),rec2qhyper=true,sumr
ange=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,F1\"
\"\"F0F8F-F8)F.\"\"#F8F,F,-F36%*(F1F8F0F8F.F8F(,&%\"nGF,F/F)F,-F36%*&*
,F+F8F1F8F0F8F-F8F9F8F8F(!\"\"F(F>F,-F36%*&F+F8F7FDF(F>F,-F36%*&F(F,F.
F8F(F>F,-F36%*(F0F8F-F8F.F8F(F>F,-F36%*(F1F8F-F8F.F8F(F>F,)F7F>F,F8*.,
&F(F)*,F+F8F1F8F0F8F-F8F9F8F,\"\"\",&F(F)*,F7F8F1F8F0F8F-F8F.F8F,\"\"
\"-F36%FWF(F/\"\"\"-F36%F(F(F>\"\"\"-F36%F6F(F>\"\"\"-F36%*&*,F+F8F-F8
F.F8F0F8F1F8F8F(FDF(F>\"\"\"FD" }}}{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)/(qpoch
hammer(q,b*c,b*d,c*d,q,k)*qpochhammer(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#>%$RHSG
*&*0-%,qpochhammerG6%*&%&alphaG\"\"\"%\"aG!\"\"%\"qG,&%\"nG\"\"\"%\"kG
!\"\"F2-F(6%*,F+F2%\"bGF2%\"cGF2%\"dGF2)F/,&F1F2F4F2F2F/F3F2-F(6%*&F8F
,F9F,F/F1F2-F(6%*&F8F,F:F,F/F1F2-F(6%*&F9F,F:F,F/F1F2)F-F0F2-F(6%F/F/F
1F2F,*0-F(6%F/F/F3\"\"\"-F(6%F?F/F3\"\"\"-F(6%FBF/F3\"\"\"-F(6%FEF/F3
\"\"\"-F(6%*,F-F2F8F,F9F,F:F,)F/,&F3F2F4F2F2F/F3\"\"\"-F(6%F/F/F0\"\"
\"-F(6%*,F-F,F8F,F9F,F:F,)F/,$F3\"\"#F2F/F0\"\"\"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),rec2qhyper=tr
ue):\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+\"\"\"%\"bGF,F1F7F.F7)F
/\"\"#F7F,F,-F36%*(F+F7F1F7F/F7F(,&%\"nGF,F0F)F,-F36%*&*,F+F7F-F7F.F7F
9F7F1F7F7F(!\"\"F(F>F,-F36%*&F-F7F8FDF(F>F,-F36%*&F(F,F/F7F(F>F,-F36%*
(F1F7F.F7F/F7F(F>F,-F36%*(F+F7F.F7F/F7F(F>F,)F8F>F,F7*.,&F(F)*,F+F7F-F
7F.F7F9F7F1F7F,\"\"\",&F(F)*,F+F7F8F7F1F7F.F7F/F7F,\"\"\"-F36%FWF(F0\"
\"\"-F36%F(F(F>\"\"\"-F36%F6F(F>\"\"\"-F36%*&*,F+F7F-F7F.F7F/F7F1F7F7F
(FDF(F>\"\"\"FD" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "RE3:=qs
umrecursion(c(k,N+k,a,b,c,d,a,b,gamma,j),q,j,S(N),rec2qhyper=true):\nf
inal3:= subs(N=n-k,rhs(RE3[1]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%
'final3G*&*6,&%\"qG!\"\"*,%\"aG\"\"\"%\"dGF,)F(%\"kGF,%&gammaGF,%\"bGF
,F,F,-%,qpochhammerG6%F*F(F/F,,&F(F)*,F+\"\"\"F1F7%\"cGF,F-F7)F.\"\"#F
7F,F,-F36%*&F0F7F8!\"\"F(,&%\"nGF,F/F)F,-F36%*(F+F7F1F7F.F7F(F?F,-F36%
*&*,F+F7F1F7F0F7F-F7F9F7F7F(F>F(F?F,-F36%*&F(F,F.F7F(F?F,-F36%*(F1F7F-
F7F.F7F(F?F,-F36%*(F+F7F-F7F.F7F(F?F,)F8F?F,F7*.,&F(F)*,F+F7F1F7F0F7F-
F7F9F7F,\"\"\",&F(F)*,F+F7F1F7F8F7F-F7F.F7F,\"\"\"-F36%FWF(F/\"\"\"-F3
6%F(F(F?\"\"\"-F36%F6F(F?\"\"\"-F36%*&*,F+F7F-F7F.F7F0F7F1F7F7F(F>F(F?
\"\"\"F>" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Section 4" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 82 "TIME:=time(): Sn:=qrecsolve(qDixon_RE,q,S(n)
,return=qhypergeometric);\ntime()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#SnG7#7$*&-%,qpochhammerG6%)%\"qG,(\"\"\"F.%\"cGF.%\"bGF.F,%\"
nG\"\"\"-F)6%F,F,F1!\"\"1\"\"!F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$
\"'&\\Y\"!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "TIME:=time
(): Sn:=qrecsolve(qDixon_RE,q,S(n),return=qhypergeometric,split=false)
;\ntime()-TIME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#SnG7#7$*&-%,qpoc
hhammerG6%)%\"qG,(%\"bG\"\"\"%\"cGF/F/F/F,%\"nG\"\"\"-F)6%F,F,F1!\"\"1
\"\"!F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&&)>%!\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "qsimplify(Sn[1][1]*qpochhammer(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&6%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)*qpochh
ammer(a,q,k)/qpochhammer(q,q,k),q,F(k));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#7#,$*&*&,&)%\"qG%\"kG\"\"\"!\"\"F+F+-%,qpochhammerG6%%\"aGF)F*F+
\"\"\"-F.6%F)F)F*!\"\"F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 
"qrecsolve(q^2*q^(2*n)*F(n+3)+(1+q)*q^n*F(n+2)+(1-q^n)*F(n+1)-F(n),q,F
(n),solution=series);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#-%$SumG6$*&
*(%$_C1G\"\"\")%\"qG*$)%#_iG\"\"#\"\"\"F*))F,%\"nGF/F*F1-%,qpochhammer
G6%F,F,F/!\"\"/F/;\"\"!%)infinityG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 72 "qrecsolve((a*q^k-1)*X(k)-a*q^n*(q^k-1)*X(k-1)=1,q,X(k
),solution=series);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#-%$SumG6$*&*(
)%\"qG%#_iG\"\"\"-%,qpochhammerG6%)F*,$%\"nG!\"\"F*F+F,))F*%\"kGF+F,\"
\"\"*&-F.6%*&F0F7%\"aG!\"\"F*F+\"\"\",&*&F<F,)F*F2F,F,F)F3\"\"\"F=/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\"
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F@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "60 0 0" 
60 }{VIEWOPTS 1 1 0 3 2 1804 }