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{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "read `c:/koepf/maple/buch/hsum.mpl`
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%ZCopyright~1998~~Wolfram~Koepf,~
Konrad-Zuse-Zentrum~BerlinG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
36 "rec2poly(n*s(n+1)-(n+20)*s(n),s(n));" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#*L&%&deltaG6#\"\"!\"\"\"%\"nGF(,&F)F(\"#>F(F(,&F)F(\"#=F(F(,&F)F
(\"#<F(F(,&F)F(\"#;F(F(,&F)F(\"#:F(F(,&F)F(\"#9F(F(,&F)F(\"#8F(F(,&F)F
(\"#7F(F(,&F)F(\"#6F(F(,&F)F(\"#5F(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(\"\"$F(
F(,&F)F(\"\"#F(F(,&F)F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 36 "rec2poly(n*s(n+1)-(n+40)*s(n),s(n));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#*^p&%&deltaG6#\"\"!\"\"\"%\"nGF(,&F)F(\"#RF(F(,&F)F(\"#
QF(F(,&F)F(\"#PF(F(,&F)F(\"#OF(F(,&F)F(\"#NF(F(,&F)F(\"#MF(F(,&F)F(\"#
LF(F(,&F)F(\"#KF(F(,&F)F(\"#JF(F(,&F)F(\"#IF(F(,&F)F(\"#HF(F(,&F)F(\"#
GF(F(,&F)F(\"#FF(F(,&F)F(\"#EF(F(,&F)F(\"#DF(F(,&F)F(\"#CF(F(,&F)F(\"#
BF(F(,&F)F(\"#AF(F(,&F)F(\"#@F(F(,&F)F(\"#?F(F(,&F)F(\"#>F(F(,&F)F(\"#
=F(F(,&F)F(\"#<F(F(,&F)F(\"#;F(F(,&F)F(\"#:F(F(,&F)F(\"#9F(F(,&F)F(\"#
8F(F(,&F)F(\"#7F(F(,&F)F(\"#6F(F(,&F)F(\"#5F(F(,&F)F(\"\"*F(F(,&F)F(\"
\")F(F(,&F)F(\"\"(F(F(,&F)F(\"\"'F(F(,&F)F(\"\"&F(F(,&F)F(\"\"%F(F(,&F
)F(\"\"$F(F(,&F)F(\"\"#F(F(,&F)F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "gosper((-1)^k/k!,k);" }}{PARA 8 "" 1 "" {TEXT -1 63 "
Error, (in gosper) no hypergeometric term antidifference exists" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "rec2hyper((n+2)*DN(n+2)-(n+1
)*DN(n+1)-(n+1)*DN(n),DN(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "rec:=\nsumrecursion(hyper
term([-n,a,a+1/2,b],[2*a,(b-n+1)/2,(b-n)/2+1],1,k),k,s(n));" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%$recG/,(*,,(\"\"#\"\"\"%\"nGF*%\"bGF*F*,(F
,!\"\"F+F*F*F*F*,&F,F.F+F*F*,(F+F*%\"aGF)F*F*F*-%\"sG6#,&F+F*F)F*F*F**
,,(F+F*F*F*F,F*F*F/\"\"\",(F+F*F*F*F1F*F*,*F1F)F,F.F+F*F*F*F*-F36#,&F+
F*F*F*F*!\"#*,F=F*,&F+F*F,F*F*F:F8,(F1F)F+F*F,F.F*-F36#F+F*F*\"\"!" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "rec2hyper(rec,s(n));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<$*&*(,(%\"aG\"\"#%\"nG\"\"\"%\"bG!\"
\"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/*&F1\"\"\"F5\"\"\"F7" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "rec:=\nsumrecursion(hyperterm([-n,a
,a+1/2,b],[2*a+1,(b-n)/2,(b-n+1)/2],1,k),k,s(n));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%$recG/,(**,(%\"bG!\"\"%\"nG\"\"\"\"\"#F,F,,(F)F*F+F,F
,F,F,,(F+F,%\"aGF-F-F,F,-%\"sG6#,&F+F,F-F,F,F,**F.\"\"\",(F0F-\"\"$F,F
+F-F,,*F-F,F0F-F+F,F)F*F,-F26#,&F+F,F,F,F,F***F<F,F9F6,*F0F-F)F*F+F,F,
F,F,-F26#F+F,F,\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "rec
2hyper(rec,s(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$*&*&,*%\"aG\"\"
#%\"bG!\"\"%\"nG\"\"\"F,F,F,,&F+F,F,F,F,\"\"\"*&,(F+F,F'F(F,F,\"\"\",(
F)F*F+F,F,F,\"\"\"!\"\"*&F&F.F2F4" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 85 "rec:=sumrecursion(\nhyperterm([-n,a,a+1/2,b],[2*a+1,(
b-n+1)/2,(b-n)/2+1],1,k),k,s(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>
%$recG/,(*.,(\"\"#\"\"\"%\"nGF*%\"aGF)F*,(%\"bGF*F+F*F)F*F*,(F.!\"\"F*
F*F+F*F*,&F.F0F+F*F*,2*$)F+F)\"\"\"F**&F.F*F+F*F)F+\"\"$*$)F.F)F5F*F)F
*F,F)*$)F,F)F5!\"%F.F*F*-%\"sG6#,&F)F*F+F*F*F**,,(F+F*F*F*F.F*F*F1F5,*
F.F0F*F*F,F)F+F*F*,F*$)F+F7F5F)F3\"#6*&F,F*F4F5F)*&F4F5F.F5\"\"%F+\"#=
*(F,F5F.F5F+F5FJ*&F,F5F+F5\"#7*&F;F5F+F5!\")F6\"#5*&F+F5F9F5F)*&F,F5F.
F5FJ*&F,F5F9F5F)F,FNF8F7\"\")F**$)F,F7F5FPF:F<F.\"\"'F*-F>6#,&F*F*F+F*
F*F0*.FenF*,&F.F*F+F*F*FCF5,(F+F*F.F0F,F)F*,2F3F*F+\"\"&F6F)F8F*F,F)FX
F*F.F7F:F<F*-F>6#F+F*F*\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "t
his calculation took 1/2 hour on a PC with Intel Pentium 200 MHz" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "TIME:=time(): rec2hyper(rec,s(n)); \+
time()-TIME;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$*&*(,*%\"bG\"\"\"%\"
aG!\"#F(F(%\"nGF(F(,&F'F(F+F(F(,(F+F(F'!\"\"F)\"\"#F(\"\"\"*(,(F'F(F)F
*F+F(\"\"\",&F'F.F+F(\"\"\",(F+F(F(F(F'F(\"\"\"!\"\"*&**,*F'F(F)F/F(F(
F+F(F(,&F(F(F+F(F(F,F0F-F0F0**,(F'F(F)F/F+F(\"\"\",(F(F(F+F(F)F/\"\"\"
F4\"\"\"F6\"\"\"F8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"(&z8<!\"$" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "rec:=sumrecursion(\nhyperte
rm([-n,a,b,-1/2-a-b-n],[-a-n,-b-n,a+b+1/2],1,k),k,s(n));" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#>%$recG/,(*.,(\"\"#\"\"\"%\"nGF*%\"bGF*F*,(F+F*F
*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*-%\"sG
6#,&F+F*F)F*F*F**,F0\"\"\"F-F7,*F/F*F)F*F+F*F,F*F*,2F/\"\"'*&F/F*F,F*
\"\"%*&F/F7F+F*F<\"\"&F**$)F+F)F7F)F+F:F,F:*&F,F7F+F7F<F*-F36#,&F+F*F*
F*F*!\"\"*.FDF*,(F+F*F*F*F,F)F*,(F+F*F/F)F*F*F*F8F7,*F/F*F+F*F*F*F,F*F
*-F36#F+F*F*\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "rec2hy
per(rec,s(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$*&*(,(%\"nG\"\"\"%
\"aG\"\"#F(F(F(,(F'F(F(F(%\"bGF*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.*&F0\"\"\"F4\"\"\"F6" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 82 "rec:=sumrecursion(\nhyperterm([-n,a,b,1/2-a-b-n],[-a-
n,1-b-n,a+b+1/2],1,k),k,s(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$r
ecG/,(*.,(%\"nG\"\"\"F*F*%\"bGF*F*,&F)F*F+F*F*,(%\"aGF*F)F*\"\"#F*F*,(
F.F*F)F*F*F*F*,*F.F/F)F*F*F*F+F/F*-%\"sG6#,&F)F*F/F*F*F**,F0\"\"\"F,F7
,2*&F.F*F)F*F/F.F/*&F.F7F+F*F/*$)F)F/F7F*F)F/*&F+F7F)F7F/F+\"\"$F*F*F*
,*F.F*F)F*F*F*F+F*F*-F36#,&F)F*F*F*F*!\"#*.,&F)F*F+F/F*FBF*,(F)F*F.F/F
*F*F*F?F7,(F.F*F)F*F+F*F*-F36#F)F*F*\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 20 "rec2hyper(rec,s(n));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#<$*.,(%\"nG\"\"\"F'F'%\"aG\"\"#F',&%\"bGF)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
0F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "rec:=sumrecursion(\n
hyperterm([-n,a,b,1/2-a-b-n],[1-a-n,1-b-n,a+b-1/2],1,k),k,s(n));" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$recG/,(*.,(%\"bG\"\"\"%\"nGF*F*F*F*
,&F)F*F+F*F*,(F+F*%\"aGF*F*F*F*,&F+F*F.F*F*,(F+F*F)\"\"#F.F1F*-%\"sG6#
,&F+F*F1F*F*F**.,&F+F*F*F*F*,&F+F*F)F1F*,&F+F*F.F1F*,*F+F*F*F*F)F*F.F*
F*,(F+F*F)F*F.F*F*-F36#F+F*F**,F,F*F/F*F:F*,0*$F+F1F**&F.F*F+F*F1*&F+F
*F)F*F1F+F*F)F1F.F1*&F)F*F.F*F1F*-F36#F7F*!\"#\"\"!" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 20 "rec2hyper(rec,s(n));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<$*.,&%\"nG\"\"\"%\"bG\"\"#F',&F&F'%\"aGF)F',(F&F'F(F'F
+F'F',&F(F'F&F'!\"\",&F&F'F+F'F.,*F&F'F.F'F+F)F(F)F.**,&F&F'F'F'F'F,F'
F-F.F/F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "rec:=sumrecursi
on(\nhyperterm([-n,a,b,3/2-a-b-n],[1-a-n,1-b-n,a+b+1/2],1,k),k,s(n));
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$recG/,(*0,(%\"bG\"\"\"%\"nGF*F*
F*F*,&F)F*F+F*F*,(F+F*%\"aGF*F*F*F*,&F+F*F.F*F*,(F+F*F)\"\"#F.F1F*,*F+
F1\"\"$F*F.F1F)F1F*-%\"sG6#,&F+F*F1F*F*F**0,&F+F*F*F*F*,&F+F*F)F1F*,&F
+F*F.F1F*,*F+F*F*F*F)F*F.F*F*,(F+F*F)F*F.F*F*,*!\"\"F*F.F1F)F1F+F1F*-F
56#F+F*F**.F,F*F/F*,0*$F+F1F**&F.F*F+F*F1*&F+F*F)F*F1F+F*F)F1F.F1*&F)F
*F.F*F1F*,*F.F1F*F*F)F1F+F1F*F<F*-F56#F9F*!\"#\"\"!" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 20 "rec2hyper(rec,s(n));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#<$*.,&%\"nG\"\"\"F'F'F',(F&F'%\"bGF'%\"aGF'F',*!\"\"F'F
*\"\"#F)F-F&F-F',*F*F-F'F'F)F-F&F-F,,&F&F'F*F'F,,&F)F'F&F'F,*2F(F',&F&
F'F)F-F',&F&F'F*F-F'F+F'F.F,,*F&F'F,F'F*F-F)F-F,F/F,F0F," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "rec:=sumrecursion(\nhyperterm([-n,a
,b,3/2-a-b-n],[1-a-n,2-b-n,a+b-1/2],1,k),k,s(n));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%$recG/,(*.,&%\"bG\"\"\"%\"nGF*F*,(F)F*F+F*!\"\"F*F*,(
F+F*%\"aGF*F*F*F*,&F+F*F/F*F*,*F+F*F-F*F/\"\"#F)F2F*-%\"sG6#,&F+F*F2F*
F*F**.,&F+F*F*F*F*,(F+F*F)F2F-F*F*,&F+F*F/F2F*,(F+F*F)F*F/F*F*,*F+F*F-
F*F/F*F)F*F*-F46#F+F*F**,F,F*F0F*,0*&F/F*F+F*F2*&F)F*F/F*F2F/F**$F+F2F
*F-F*F)F2*&F+F*F)F*F2F*F;F*-F46#F8F*!\"#\"\"!" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "rec2hyper(rec,s(n));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<$*.,*%\"nG\"\"\"!\"\"F'%\"aGF'%\"bGF'F',(F&F'F*\"\"#F(
F'F',&F&F'F)F,F',(F*F'F&F'F(F'F(,&F&F'F)F'F(,*F&F'!\"#F'F)F,F*F,F(**,&
F&F'F'F'F'F%F'F.F(F/F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "r
ec:=sumrecursion(\nhyperterm([-n,a,b,5/2-a-b-n],[2-a-n,2-b-n,a+b-1/2],
1,k),k,s(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$recG/,(*0,&%\"bG\"
\"\"%\"nGF*F*,(F)F*F+F*!\"\"F*F*,&F+F*%\"aGF*F*,(F+F*F/F*F-F*F*,*F/\"
\"#F*F*F)F2F+F2F*,*F+F*!\"#F*F)F2F/F2F*-%\"sG6#,&F+F*F2F*F*F**0,&F+F*F
*F*F*,(F+F*F)F2F-F*F*,(F+F*F/F2F-F*F*,*!\"$F*F/F2F)F2F+F2F*,(F+F*F)F*F
/F*F*,*F+F*F-F*F/F*F)F*F*-F66#F+F*F**.F,F*F0F*,*F-F*F/F2F)F2F+F2F*,2*&
F/F*F+F*\"\"%F/F2*&F)F*F/F*FG*$F+F2F2F+F4F>F*F)F2*&F+F*F)F*FGF*F?F*-F6
6#F:F*F-\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "rec2hyper(
rec,s(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$*2,*%\"nG\"\"\"!\"\"F'
%\"aGF'%\"bGF'F',*!\"$F'F)\"\"#F*F-F&F-F',(F&F'F*F-F(F'F',(F&F'F)F-F(F
'F',(F*F'F&F'F(F'F(,(F&F'F)F'F(F'F(,*F&F'F,F'F)F-F*F-F(,*F(F'F)F-F*F-F
&F-F(*.,&F&F'F'F'F'F%F'F+F'F0F(F1F(F3F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "recpoly(n*(n+1)*s(n+3)-2*n*(n+3)*s(n+1)+(n+1)*(n+3)*s
(n),s(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&&%&deltaG6#\"\"!\"\"\"
%\"nGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "rechyper((n+1+2*
b)*(n+2*b)*s(n+2)-4*(n+b)*(n+1+b)*s(n),s(n));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<$,$*&,&%\"nG\"\"\"%\"bGF(\"\"\",&F'F(F)\"\"#!\"\"!\"#,
$F%F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "rechyper(\n(n+1+2*
b)*(n+2+2*b)*(n+2*b)*s(n+3)-8*(n+2+b)*(n+1+b)*(n+b)*s(n),s(n));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<%*&*&,&!\"\"\"\"\"*&%\"IGF(-%%sqrtG6#
\"\"$\"\"\"F(F(,&%\"nGF(%\"bGF(F(F/,&F1F(F2\"\"#!\"\",$*&F0F/F3F5F4,$*
&*&,&F(F(F)F(F(F0F/F/F3F5F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
99 "rechyper((n+2+2*b)*(n+2*b)*(n+3+2*b)*(n+1+2*b)*s(n+4)-\n16*(n+3+b)
*(n+2+b)*(n+1+b)*(n+b)*s(n),s(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
<&,$*&*&%\"IG\"\"\",&%\"nGF(%\"bGF(F(\"\"\",&F*F(F+\"\"#!\"\"F.,$*&F)F
,F-F/!\"#,$F1F.,$F%F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "sh
arename:=\"c:\\\\PROGRAMME\\\\Maple V Release 5 Share Library\\\\Share
\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(share):" }}
{PARA 6 "" 1 "" {TEXT -1 70 "See ?share and ?share,contents for inform
ation about the share library" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "with(gfun);" }}{PARA 6 "" 1 "" {TEXT -1 20 "Share Library:  gfun
" }}{PARA 6 "" 1 "" {TEXT -1 43 "Authors: Salvy, Bruno and Zimmermann,
 Paul." }}{PARA 6 "" 1 "" {TEXT -1 80 "Description:  package for the m
anipulation and discovery of generating functions" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#7V%(LaplaceG%.algebraicsubsG%.algeqtodiffeqG%.algeqtose
riesG%.algfuntoalgeqG%&borelG%.cauchyproductG%.diffeq*diffeqG%.diffeq+
diffeqG%2diffeqtohomdiffeqG%,diffeqtorecG%)guesseqnG%(guessgfG%0hadama
rdproductG%0holexprtodiffeqG%)invborelG%,listtoalgeqG%-listtodiffeqG%0
listtohypergeomG%+listtolistG%.listtoratpolyG%*listtorecG%-listtoserie
sG%5listtoseries/LaplaceG%1listtoseries/egfG%4listtoseries/lgdegfG%4li
sttoseries/lgdogfG%1listtoseries/ogfG%4listtoseries/revegfG%4listtoser
ies/revogfG%,maxdegcoeffG%*maxdegeqnG%,maxordereqnG%,mindegcoeffG%*min
degeqnG%,minordereqnG%*optionsgfG%,poltodiffeqG%)poltorecG%/ratpolytoc
oeffG%(rec*recG%(rec+recG%,rectodiffeqG%,rectohomrecG%*rectoprocG%.ser
iestoalgeqG%/seriestodiffeqG%2seriestohypergeomG%-seriestolistG%0serie
storatpolyG%,seriestorecG%/seriestoseriesG" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 161 "diffeq:=a*(1-z)*z*diff(F(z),z$3)+(a+a^2+a*b+z-3*a*
z-3*a^2*z-2*z^2+z^3)* \ndiff(F(z),z$2)+ (-3*a^2-2*a^3+b-z-4*a*z-b*z+z^
2+3*a*z^2)*diff(F(z),z)+\n2*a^2*(z-1)*F(z);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%'diffeqG,***%\"aG\"\"\",&F(F(%\"zG!\"\"F(F*F(-%%diffG
6$-%\"FG6#F*-%\"$G6$F*\"\"$F(F(*&,2F'F(*$)F'\"\"#\"\"\"F(*&F'F;%\"bGF(
F(F*F(*&F'F;F*F;!\"$*&F9F;F*F;F?*$)F*F:F;!\"#*$)F*F5F;F(F(-F-6$F/-F36$
F*F:F(F(*&,2F8F?*$)F'F5F;FCF=F(F*F+F>!\"%*&F=F;F*F;F+FAF(*&F'F;FBF;F5F
(-F-6$F/F*F(F(*(F9F;,&F*F(F+F(F(F/F(F:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "rec:=diffeqtorec(diffeq,F(z),u(n));" }}{PARA 12 "" 1 
"" {XPPMATH 20 "6#>%$recG<&,**&,(*$)%\"aG\"\"#\"\"\"F,*&%\"nG\"\"\"F+F
0\"\"$*$)F/F,F-F0F0-%\"uG6#F/F0F0*&,.F2!\"#*&,(!\"$F0F+!\"%%\"bG!\"\"F
0F/F-F0F)F9F?F0F+F=F>F?F0-F56#,&F/F0F0F0F0F0*&,2*&F+F-)F/F1F-F?*&,(F+!
\"'F0F0F)F<F0F3F-F0*&,,*$)F+F1F-F9F)!#7F+!#6F>F0F1F0F0F/F-F0F,F0F)FNFL
F=F>F,F+FIF0-F56#,&F/F0F,F0F0F0*&,.FEF0*&,(*&F+F-F>F0F0F)F0F+\"\"(F0F3
F-F0*&,(FW\"\"&F)FenF+\"#;F0F/F-F0FW\"\"'F)FgnF+\"#7F0-F56#,&F/F0F1F0F
0F0/-F56#\"\"!,$*&,.*&&%#_CGF^oF0F*F-F1*&FdoF-FMF-F,*&FdoF-F>F-F?*&&Fe
o6#F0F0F+F-F9*&FioF-F*F-F9*(FioF-F+F-F>F-F9F-*$)F+\"\"#F-!\"\"#F?F,/-F
56#F,Fio/-F5FjoFdo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "rec:=
op(1,rec);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$recG,**&,(*$)%\"aG\"
\"#\"\"\"F+*&%\"nG\"\"\"F*F/\"\"$*$)F.F+F,F/F/-%\"uG6#F.F/F/*&,.F1!\"#
*&,(!\"$F/F*!\"%%\"bG!\"\"F/F.F,F/F(F8F>F/F*F<F=F>F/-F46#,&F.F/F/F/F/F
/*&,2*&F*F,)F.F0F,F>*&,(F*!\"'F/F/F(F;F/F2F,F/*&,,*$)F*F0F,F8F(!#7F*!#
6F=F/F0F/F/F.F,F/F+F/F(FMFKF<F=F+F*FHF/-F46#,&F.F/F+F/F/F/*&,.FDF/*&,(
*&F*F,F=F/F/F(F/F*\"\"(F/F2F,F/*&,(FV\"\"&F(FZF*\"#;F/F.F,F/FV\"\"'F(F
fnF*\"#7F/-F46#,&F.F/F0F/F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "rechyper(rec,u(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#*&*&,&%
\"nG\"\"\"%\"aG\"\"#F(,&F'F(F)F(F(\"\"\"*&,&F'F(F(F(\"\"\",(F'F(F)F(%
\"bGF(\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "rec2hy
per(\n(-1+n)*(2+n)*s(n)+(1-11*n-2*n^2)*s(n+1)+(2+n)*(8+n)*s(n+2),s(n))
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#*&,&%\"nG\"\"\"\"\"#F'\"\"\",&
\"\"(F'F&F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "rec:=su
mrecursion(\n(-1)^k*binomial(r-s-k,k)*binomial(r-2*k,n-k)/(r-n-k+1),k,
s(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$recG/,(**,&%\"nG\"\"\"\"
\"#F*F*,(F)!\"#!\"$F*%\"rGF*F*,*F)F*F*F*F/!\"\"%\"sGF*F*-F26#F(F*F**(,
(F/F*F)F-F1F*F*,.*&F/F*F)F*F+F/F+*&F2F*F/\"\"\"F1F)F-*$)F2F+F:F**$)F)F
+F:F-F*-F26#,&F)F*F*F*F*F1**,(F/F*F)F1F*F*F*,(F/F*F)F-F*F*F*,&F)F1F2F*
F*-F26#F)F*F*\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "rec2h
yper(rec,s(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$*&*&,(%\"rG\"\"\"
%\"nG!\"#F(F(F(,&F)!\"\"%\"sGF(F(\"\"\"*&,&F)F(F(F(\"\"\",(F'F(F)F*F,F
(\"\"\"!\"\"*&*&,(F'F(F)F,F(F(F(F&F.F.*&,(F'F,F-F(F)F(\"\"\"F2\"\"\"F4
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "ratio(binomial(s,n)/(r-
2*n+1),n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*&,(%\"rG\"\"\"%\"nG!
\"#F'F'F',&F(!\"\"%\"sGF'F'\"\"\"*&,&F(F'F'F'\"\"\",(F&F'F(F)F+F'\"\"
\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "rec:=sumrecursi
on(binomial(n,k)*pochhammer(c,k)*pochhammer(m,n-k)*\nhyperterm([-k,a,b
],[c,d],1,j),j,s(k));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$recG/,(*,,
&%\"kG\"\"\"\"\"#F*F*,*%\"mGF*%\"nGF*F)!\"\"F/F*F*,*F-F*F.F*F)F/!\"#F*
F*,(F)F*F*F*%\"dGF*F*-%\"sG6#F(F*F***,(F.F*F)F/F/F*F*,<F*F**&%\"aGF*F)
F*F/*&%\"bGF*F)\"\"\"F/*$)F)F+F>F+*&F)F>%\"cGF*F+*&F)F>F3F*F+F=F/*&FBF
>F3F>F*F;F/F3F+FBF+*&F;F>F=F>F/F)\"\"$F*F,F>-F56#,&F)F*F*F*F*F/*,,,F;F
/F=F/F)F*FBF*F3F*F*F8F>,&F.F*F)F/F*,&FBF*F)F*F*-F56#F)F*F*\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "rec2hyper(rec,s(k));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "rec2hyper((n+2)*H(n+2)-(2*n+3)*H(n+1)+(n+1)*H(n),H(n)
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#\"\"\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 36 "read `c:/koepf/maple/buch/qsum.mpl`;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%OCopyright~1998,~~Harald~Boeing~&~Wolfram~K
oepfG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%;Konrad-Zuse-Zentrum~BerlinG
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Rogers" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 93 "RE:=qsumrecursion((-1)^k*q^(k*(3*k-1)/2)/qpochhammer(
q,q,n+k)/qpochhammer(q,q,n-k),q,k,S(n));" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#>%#REG/,**,%\"qG\"\"\",&F)F))F(%\"nGF)F),&)F(,$F,\"\"#!\"\"F(F)F
),&F+F)F1F)F)-%\"SG6#F,F)F1*&,.)F(,&F,F0F0F)F)*$)F(\"\"$\"\"\"F1*$)F(
\"\"%F=F1*$)F(F0F=F1)F(,&F,F<F)F)F))F(,$F,F<F)F)-F46#,&F,F)F1F)F)F)*(,
*FAF)F.F)F:F)F>F)F)F(F=-F46#,&F,F)!\"#F)F)F)*&)F(\"\"&F=-F46#,&F,F)!\"
$F)F)F1\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "qrecsolve(R
E,q,S(n),return=qhypergeometric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7
#7$*&\"\"\"F&-%,qpochhammerG6%%\"qGF*%\"nG!\"\"1\"\"!F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "F:=(-1)^k*q^(k*(3*k-1)/2)/qpochhamm
er(q,q,n+k)/qpochhammer(q,q,n-k):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "rat:=qsimpcomb(subs(k=-k,F)/F);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$ratG)%\"qG%\"kG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "qsumrecursion((1+rat)/2*F,q,k,S(n));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/,&*&,&)%\"qG%\"nG\"\"\"!\"\"F*F*-%\"SG6#F)F*F*-F-
6#,&F)F*F+F*F*\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "(9.17)" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "leftRE:=qsumrecursion(q^(k^2+k)/qpo
chhammer(q,q,k)/qpochhammer(q,q,n-k),q,k,S(n));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%'leftREG/,(*&,&)%\"qG%\"nG\"\"\"!\"\"F,F,-%\"SG6#F+F,
F,*&,*F*F,)F*,$F+\"\"#F,F)F-F,F,F,-F/6#,&F+F,F-F,F,F,*&F*F,-F/6#,&F+F,
!\"#F,F,F-\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "rightRE
:=qsumrecursion((-1)^k*q^(k*(5*k+3)/2)/qpochhammer(q,q,n+k+1)/qpochham
mer(q,q,n-k),q,k,S(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(rightREG
/,.*,)%\"qG\"\"#\"\"\",&\"\"\"F-)F)%\"nGF-F-,&F.F-!\"\"F-F-,&F1F-)F),&
F-F-F/F*F-F--%\"SG6#F/F-F1*(,6*$F(F+F-F)F-*$)F)\"\"&F+F-)F),&\"\"%F-F/
F*F1)F),&F/F*\"\"$F-F1*$)F)FCF+F-)F),&F/F*F*F-F1)F),$F/F=F1)F),&F*F-F/
F=F1*$)F)F@F+F-F-F)F--F66#,&F/F-F1F-F-F-*&,<)F),&F-F-F/F@F1FFF1FLF1FDF
1*$)F)\"\")F+F1*$)F)\"\"(F+!\"#*$)F)\"\"*F+F1)F),$F/\"\"'F1F;FenF>F1FA
F1)F),&F/F@F*F-F1*$)F)F[oF+FenF--F66#,&F/F-FenF-F-F-*(F)F+,@F\\oF-FFF-
FSF-)F),$F/F@F-FLF-FAF*F>F*F^oF*F;F-*$)F)\"#5F+F-FfnF-FXF*)F),&F[oF-F/
F*F-)F),&F=F-F/F*F-FUF*F--F66#,&F/F-!\"$F-F-F-*(,2)F),$F/F*F-FFF-FDF-F
^oF-FLF-FXF-F3F-F;F-F-F<F+-F66#,&F/F-!\"%F-F-F1*&)F)\"#7F+-F66#,&F/F-!
\"&F-F-F-\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "`recursio
n/compare`(leftRE,rightRE,S(n));" }}{PARA 6 "" 1 "" {TEXT -1 42 "Warni
ng: Different recursion orders. (2,5)" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#%;Recursions~are~compatible.G" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 78 "rightterm:=(-1)^k*q^(k*(5*k+3)/2)/qpochhammer(q,q,n+k
+1)/qpochhammer(q,q,n-k):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
47 "rat:=qsimpcomb(subs(k=-k,rightterm)/rightterm);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$ratG,$*&,&!\"\"\"\"\"*(%\"qGF))F+%\"nGF))F+%\"kGF)
F)\"\"\"*&)F.\"\"#F0,&F.F)*&F,F0F+F0F(\"\"\"!\"\"F(" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 53 "rightRE:=qsumrecursion((1+rat)/2*rightter
m,q,k,S(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(rightREG/,(*&,&)%\"
qG%\"nG\"\"\"!\"\"F,F,-%\"SG6#F+F,F,*&,*F*F,)F*,$F+\"\"#F,F)F-F,F,F,-F
/6#,&F+F,F-F,F,F,*&F*F,-F/6#,&F+F,!\"#F,F,F-\"\"!" }}}{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 18 "version of q-Dixon" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 114 "RE:=qsumrecursion((-1)^k*qbinomial(n+b,n+k,q)
*qbinomial(n+c,c+k,q)*qbinomial(b+c,b+k,q)*q^(k*(3*k-1)/2),q,k,S(n));
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#REG/,**,)%\"qG\"\"$\"\"\",&\"\"
\"F-)F)%\"nGF-F-,&)F),$F/\"\"#!\"\"F)F-F-,&F.F-F4F-F--%\"SG6#F/F-F-*(F
)F-,J*$)F)\"\"&F+F-)F),*\"\"%F-F/F-%\"cGF-%\"bGF-F4*$)F)F@F+F-)F),(F*F
-F/F3FAF-F-)F),(F*F-F/F3FBF-F-)F),&F*F-F/F3F4)F),*F*F-F/F-FAF-FBF-F4)F
),(F*F-F/F-FAF-F4)F),(F*F-F/F-FBF-F4*$F(F+F-)F),&F/F*F3F-F4)F),(F/F*F3
F-FAF-F4)F),(F/F*F3F-FBF-F4)F),*F/F3F3F-FAF-FBF-F4)F),(F/F3FBF-F3F-F-)
F),(F/F3F3F-FAF-F-)F),*FBF-FAF-F3F-F/F@F-)F),&F/F*F-F-F4)F),*F/F@F-F-F
AF-FBF-F-)F),(F/F@FAF-FBF-F-F--F76#,&F/F-F4F-F-F-*(,B*$)F)\"\"'F+F-F;F
-F>F4)F),(F@F-F/F-FBF-F4FCF-)F),(F@F-F/F-FAF-F4FGF-FEF-FOF4FMF4FZF-Ffn
F-)F),&F/F3F3F-F-)F),*F/F*F3F-FAF-FBF-F4)F),*F/F*F-F-FAF-FBF-F4)F),(F/
F*FAF-FBF-F4F-,&)F),(F/F-FAF-FBF-F4F)F-F--F76#,&F/F-!\"#F-F-F4*,,&*$)F
)F3F+F-)F),&F/F-FAF-F4F-,&FepF4F]qF-F-,&F]qF-)F),&F/F-FBF-F4F-FdpF+-F7
6#,&F/F-!\"$F-F-F-\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "
TIME:=time():\nqrecsolve(RE,q,S(n),return=qhypergeometric);\ntime()-TI
ME;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7$*&-%,qpochhammerG6%)%\"qG,(
\"\"\"F,%\"cGF,%\"bGF,F*%\"nG\"\"\"-F'6%F*F*F/!\"\"1\"\"!F/" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"'km6!\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 89 "F:=(-1)^k*qbinomial(n+b,n+k,q)*qbinomial(n+c,c+k,q)*q
binomial(b+c,b+k,q)*q^(k*(3*k-1)/2):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "rat:=qsimpcomb(subs(k=-k,F)/F);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$ratG)%\"qG%\"kG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "RE2:=qsumrecursion((1+rat)/2*F,q,k,S(n));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$RE2G/,&*&,&\"\"\"F))%\"qG%\"nG!\"\"F)-%\"
SG6#F,F)F)*&,&)F+,(F,F)%\"cGF)%\"bGF)F)F-F)F)-F/6#,&F,F)F-F)F)F)\"\"!
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "assume(n,integer);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "sum2qhyper(F,q,k);" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#*&**-%,qpochhammerG6%%\"qGF(,&%#n|irG\"\"\"%
\"bGF+F+-F&6%F(F(,&F*F+%\"cGF+F+-F&6%F(F(,&F,F+F0F+F+-%$phiG6&7&)F(,$F
0!\"\")F(,$F*F:)F(,$F,F:F(7%)F(,&F+F+F0F+)F(,&F+F+F*F+)F(,&F+F+F,F+F(*
*F(F+)F(F,F+)F(F*F+)F(F0F+F+\"\"\"*()-F&6%F(F(F*\"\"#FJ)-F&6%F(F(F,\"
\"#FJ)-F&6%F(F(F0\"\"#FJ!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 7 "n:='n':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "sum2qhyper(
subs(k=k-n,F),q,k);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*&**)!\"\",$%\"
nGF&\"\"\"-%,qpochhammerG6%%\"qGF-,&%\"bGF)%\"cGF)F))F-,&*$)F(\"\"#\"
\"\"#\"\"$F5F(#F)F5F)-%$phiG6&7%)F-,$F(!\"#)F-,&F(F&F/F&)F-,&F0F&F(F&7
$)F-,(F)F)F(F&F0F))F-,(F)F)F(F&F/F)F-**F-F))F-F(F))F-F/F))F-F0F)F)F6*(
-F+6%F-F-,&F0F)F(F&\"\"\"-F+6%F-F-,$F(F5\"\"\"-F+6%F-F-,&F/F)F(F&\"\"
\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "sum2qhyper(subs
(k=k-n,F)/(qfactorial(n+b+c,q)/qfactorial(n,q)/qfactorial(b,q)/qfactor
ial(c,q)),q,k);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*&*0)!\"\",$%\"nGF&
\"\"\"-%,qpochhammerG6%%\"qGF-,&%\"bGF)%\"cGF)F))F-,&*$)F(\"\"#\"\"\"#
\"\"$F5F(#F)F5F)-F+6%F-F-F(F)-F+6%F-F-F/F)-F+6%F-F-F0F)-%$phiG6&7%)F-,
$F(!\"#)F-,&F(F&F/F&)F-,&F0F&F(F&7$)F-,(F)F)F(F&F0F))F-,(F)F)F(F&F/F)F
-**F-F))F-F(F))F-F/F))F-F0F)F)F6**-F+6%F-F-,&F0F)F(F&\"\"\"-F+6%F-F-,$
F(F5\"\"\"-F+6%F-F-,&F/F)F(F&\"\"\"-F+6%F-F-,(F(F)F0F)F/F)\"\"\"!\"\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "F:=qphihyperterm([q^(-2
*n),b,c],[q^(1-2*n)/b,q^(1-2*n)/c],q,q^(2-n)/b/c,k):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 34 "rat:=qsimplify(subs(k=2*n-k,F)/F);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ratG*&)%\"qG%\"nG\"\"\")F'%\"kG!\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "rec:=qsumrecursion((1
+rat)*F,q,k,S(n));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$recG/,&*.,&*&
)%\"qG,$%\"nG\"\"#\"\"\"%\"bGF/F/F+!\"\"F/,&F)F/*$)F+F.\"\"\"F1F/,&F+F
1*(F0F5)F+F-F/%\"cGF/F/F/,&*&F*F5F9F5F/F+F1F/,&F;F/F3F1F/-%\"SG6#F-F/F
/*2,&*(F*F5F9F5F0F5F/F3F1F/F+F/,&F+F1*&F8F5F9F5F/F/,&FBF/F+F1F/,&F/F/F
8F/F/,&*&F0F5F8F5F/F+F1F/,&F*F1F+F/F/-F>6#,&F-F/F1F/F/F/\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "qrecsolve(rec,q,S(n),return=
qhypergeometric);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7#7$*&*.-%,qpochh
ammerG6%%\"cG%\"qG%\"nG\"\"\"-F(6%%\"bGF+F,F--F(6%*&F0F-F*F-*$)F+\"\"#
\"\"\"F,F--F(6%*(F+F-F0F7F*F7F4F,F--F(6%F+F4F,F--F(6%,$F+!\"\"F+F,F-F7
*,-F(6%F3F+F,\"\"\"-F(6%*&F0F7F+F7F4F,\"\"\"-F(6%F0F4F,\"\"\"-F(6%*&F*
F7F+F7F4F,\"\"\"-F(6%F*F4F,\"\"\"!\"\"1\"\"!F," }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 15 "too complicated" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
26 "qsumrecursion(F,q,k,S(n));" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning
, computation interrupted" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }