{VERSION 2 3 "IBM INTEL NT" "2.3" }
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{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
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0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 702 "f:=y=x*x-c; A(0,0) \+
:= 1/y;\nB(0,0) := diff(y,x)/y;\nfor i from 1 to 3 do w := i;\nl := w;
\n# Results for A(0,w) verified correct.\nA(0,w):= simplify(sum('(-1)^
(a-1)*y^(a-1)*implicitdiff(f,y,x$w)*y^(w-a+1)*A(0,w-a)/a!','a'=1..w)/y
^(w+1));#\n# Results for B(0,w) verified correct.\nB(0,w):= simplify(s
um('(-1)^(a)*y^(a)*implicitdiff(f,y,x$(w+1))*y^(w-a+1)*A(0,w-a)/a!','a
'=1..w)/y^(w+1)); #\n# Results for A(l,w) \nA(l,w) := simplify(sum('(-
1)^(a)*(l!/(l-a)!)*x^(l-a)*y^a*y^(w-a+1)*A(0,w-a)','a'=0..min(w,w))/y^
(w+1));\n#\n# Results for B(l,w)\nB(l,w) := simplify(sum('(-1)^(a)*(l!
/(l-a)!)*x^(l-a)*y^a*y^(w-a+1)*B(0,w-a)','a'=0..min(w,w))/y^(w+1));\nx
prime  := x - A(l,w-1)/A(l,w);\nxxprime := x - B(l,w-1)/B(l,w);\nod;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG/%\"yG,&*$%\"xG\"\"#\"\"\"%\"c
G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!F'*$%\"yG!\"\"
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!F'F'" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"wG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"lG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"\",$*&
%\"xGF(%\"yG!\"#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"
!\"\"\",$*$%\"yG!\"\"!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$
\"\"\"F'*&,&*$%\"xG\"\"#F,%\"yG!\"\"F'F-!\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"BG6$\"\"\"F',$*&%\"xGF'%\"yG!\"\"!\"#" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%'xprimeG%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%(xxprimeG%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"#
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG\"\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"#*&,&%\"xG\"\"%%\"yG!\"\"\"\"\"F-!\"$
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"#F'" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"#F'*&,(*$%\"xG\"\"$\"\"%*&F+F'%\"y
G\"\"\"!\"&*$F/F'F'F0F/!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG
6$\"\"#F',$*&%\"xG\"\"\"%\"yG!\"\"\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%'xprimeG,&%\"xG\"\"\"**F&F',&*$F&\"\"#F'%\"yG!\"\"F'F,F',(*$F&
\"\"$\"\"%*&F&F+F,F'!\"&*$F,F+F+F-!\"#" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%(xxprimeG,$%\"xG#\"\"$\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%\"wG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG\"\"$" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"$F'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>-%\"AG6$\"\"$F',$*&,(*$%\"xGF'\"\"%*&F,\"\"#%\"yG\"\"\"!\"&*$F0F/F/
F1F0!\"$F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"$F',$*&%\"x
G\"\"\"%\"yG!\"\"!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xprimeG,&%
\"xG\"\"\"*(F&F',(*$F&\"\"$\"\"%*&F&\"\"#%\"yGF'!\"(*$F/F.\"\"'F',(F*F
,F-!\"&F1F.!\"\"#F'F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xxprimeG,$
%\"xG#\"\"$\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }