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{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<!\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=time(): result:=qgosp
er(qpochhammer(a,q,k)/qpochhammer(q,q,k)/(a*q^80)^k,q,k,simplify=false
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"6#$\"&wF$!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "TIME:=ti
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,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),$*&F,F'F&F'F'F%-F16%F)F),&%
\"bGF'F4F'F'-F16%F)F),&F<F'F&F%F%-%$phiG6&7%)F),&F&F%F<F%)F),&F&F%F4F%
)F),$*&F,F'F&F'F%7$)F),(F&F%F'F'F<F')F),(F&F%F'F'F4F'F)**F)F')F)F<F')F
)F&F')F)F4F'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*,$*&\"\"#F,F+F,F,F,F*F
-F,)F*\"\"$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,*$)F*F2F,F-F,,&)F*
,&F+F,F@F,F,F_rF-F,,&FbpF,F_rF-F,FapF,-F76#,&F+F,F4F-F,F,\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "M:=qsimpcomb(subs(k=-k,term)
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "qsumrecursion((1+M)/2*term,q
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\"\"F+F+-%\"SG6#F)F+F+*&,&)F(,(F)F+%\"bGF+%\"cGF+F+F+F*F+-F-6#,&F)F+F+
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"" 0 "" {TEXT -1 8 "(III.18)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 390 "TI
ME:=time():\nleftRE:=qsumrecursion(qpochhammer(a,q,k)*qpochhammer(a*q^
2,q^2,k)*qpochhammer(b,q,k)*qpochhammer(c,q,k)*qpochhammer(d,q,k)*qpoc
hhammer(e,q,k)*qpochhammer(q^(-n),q,k)*(a^2*q^(2+n)/(b*c*d*e))^k/(qpoc
hhammer(a,q^2,k)*qpochhammer(a/b*q,q,k)*qpochhammer(a/c*q,q,k)*qpochha
mmer(a/d*q,q,k)*qpochhammer(a/e*q,q,k)*qpochhammer(a*q^(n+1),q,k)*qpoc
hhammer(q,q,k)),q,k,S(n));\ntime()-TIME;" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#>%'leftREG/,(*.%\"qG\"\"\",&*&)F(%\"nGF)%\"aGF)F)%\"eG!\"\"F),&F
+F)%\"dGF0F),&F+F)%\"cGF0F),&F+F)%\"bGF0F)-%\"SG6#F-F)F)*(,B*&)F(,&*&
\"\"$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\"\"$F--%\"QG6#%\"nGF-F-*(,**()F0F5F-%\"aGF-F(F-F-*(F9F-%\"bGF-F(F-F-
*&F0F-)F(\"\"#F-!\"\"F0F@F-)F0F?F--F36#,&F5F-F-F@F-F-**F(F-,&*(F:F-F<F
-F9F-F-*$FAF-F@F-,&F9F-F0F@F--F36#,&F5F-F?F@F-F-\"\"!" }}}{EXCHG 
{PARA 0 "> " 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\"\"$F--%\"QG6#%\"nGF-F-*(,**()F0F5F-%\"aGF-F(F-F-*(F9F-%\"bGF-F(F-F-
*&F0F-)F(\"\"#F-!\"\"F0F@F-)F0F?F--F36#,&F5F-F-F@F-F-**F(F-,&*(F:F-F<F
-F9F-F-*$FAF-F@F-,&F9F-F0F@F--F36#,&F5F-F?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*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$F:-F66)F8F<F>F@*,9&F:9'F:9(F:F;F:)F@,&FHF:F:FGF:F@FHFG-F66%F@F@,&
FAF:FHFGFG)F@,&*$)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@,$*&FXF:FHF:F:F:*(
F9F:F;F:F_oF:*(F=F:F;F:F_oF:*(F?F:F;F:F_oF:F@F@9-F:F0F0F0" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "intermediate:=qsumrecursion(c(k,N+
k,a,b,c,d,alpha,b,c,j),q,j,S(N),rec2qhyper=true,sumrange=0..N):\nfinal
:= subs(N=n-k,rhs(intermediate[1]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "
6#>%&finalG*B,&*,%\"cG\"\"\"%\"dGF))%\"qG%\"kGF)%\"bGF)%&alphaGF)F)F,!
\"\"F)-%,qpochhammerG6%F'F,F-F),&*,%\"aGF)F.F)F(F)F*F))F+\"\"#F)F)F,F0
F),&*,F(F)F*F)F7F)F.F)F/F)F)F,F0F0,&*,F6F)F.F)F(F)F*F)F+F)F)F,F0F0-F26
%F<F,F-F0-F26%*(F(F)F+F)F.F)F,,&%\"nGF)F-F0F)-F26%*.F(F)F*F)F+F8F.F)F/
F)F,F0F,FBF)-F26%*&F/F)F6F0F,FBF)-F26%*(F.F)F*F)F+F)F,FBF)-F26%*(F(F)F
*F)F+F)F,FBF)-F26%*&F+F)F,F)F,FBF)-F26%F,F,FBF0-F26%F5F,FBF0-F26%*.F(F
)F*F)F+F)F.F)F/F)F,F0F,FBF0)F6FBF)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 228 "RHS:=qpochhammer(alpha/a,q,n-k)*qpochhammer(alpha*b*
c*d*q^(n-1),q,k)*qpochhammer(b*c,b*d,c*d,q,n)*a^(n-k)*qpochhammer(q,q,
n)/(qpochhammer(q,b*c,b*d,c*d,q,k)*qpochhammer(a*b*c*d*q^(k-1),q,k)*qp
ochhammer(q,a*b*c*d*q^(2*k),q,n-k));" }}{PARA 12 "" 1 "" {XPPMATH 20 "
6#>%$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<F.F1F--F'6%F?F.F1F--F'6%FBF.F1F--F'6%*,F,F+F5F
+F6F+F7F+)F.,&F1F+F+F-F+F.F1F--F'6%F.F.F/F--F'6%*,F,F+F5F+F6F+F7F+)F.,
$*&\"\"#F+F1F+F+F+F.F/F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Da ka
m fr\374her 1 heraus!" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "qsimpcomb(final/RHS);" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#*F-%,qpochhammerG6%*,%\"cG\"\"\"%\"dGF))%\"qG%\"kGF)%\"bGF)%&alp
haGF)F,F-F)-F%6%*(F(F)F+F)F.F)F,,&%\"nGF)F-!\"\"F)-F%6%*,F(F)F*F))F+\"
\"#F)F.F)F/F)F,F3F)-F%6%*(F.F)F*F)F+F)F,F3F)-F%6%*(F(F)F*F)F+F)F,F3F),
&)F,F4F)F)F5F)-F%6%F+F,F3F)-F%6%F,F,F-F)-F%6%*&F.F)F(F)F,F-F)-F%6%*&F.
F)F*F)F,F-F)-F%6%*&F(F)F*F)F,F-F)-F%6%F,F,F4F5-F%6%FOF,F4F5-F%6%FLF,F4
F5-F%6%FIF,F4F5-F%6%*,F/F)F.F)F(F)F*F)FBF)F,F-F5-F%6%F'F,F3F5,&F+F)F)F
5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "qsimplify(final/RHS)
;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*:-%,qpochhammerG6%*,%\"cG\"\"\"%
\"dGF)%\"qG!\"\"%\"aGF)%\"bGF)F+,$*&\"\"#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<F-F.F0-F26%*(
F/F)F*F)F,F)F-,&%\"nGF)F.F0F)-F26%*.F(F)F*F)F+F)F,F8F/F)F-F0F-FBF)-F26
%*&F(F)F6F0F-FBF)-F26%*&F,F)F-F)F-FBF)-F26%*(F*F)F+F)F,F)F-FBF)-F26%*(
F/F)F+F)F,F)F-FBF)-F26%F-F-FBF0-F26%F5F-FBF0-F26%*.F(F)F*F)F+F)F,F)F/F
)F-F0F-FBF0)F6FBF)" }}}{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,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<F,F-F0-F26%*(F.F)F/F)F+F)F,,&%\"nGF)F-F0F)-F26%*.F(F)F*F)F+F8F.F)F/
F)F,F0F,FBF)-F26%*&F6F0F*F)F,FBF)-F26%*&F+F)F,F)F,FBF)-F26%*(F/F)F(F)F
+F)F,FBF)-F26%*(F.F)F(F)F+F)F,FBF)-F26%F,F,FBF0-F26%F5F,FBF0-F26%*.F(F
)F*F)F+F)F.F)F/F)F,F0F,FBF0)F6FBF)" }}}{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),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 }