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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "with(MS):" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 22 "Consider the function " }{XPPEDIT 18 0 "s
[1](x) = x+x*exp(x);" "6#/-&%\"sG6#\"\"\"6#%\"xG,&F*\"\"\"*&F*F,-%$exp
G6#F*F,F," }{TEXT -1 63 ".  Converting this to an exponential generati
ng function gives:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "s[1] \+
:= x + x * exp(x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "conve
rt_egf(s[1], b, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&/-%\"bG6#%\"xG,
&-F%6#,&F'\"\"\"!\"\"F,\"\"#-F%6#,&F'F,!\"#F,F-F%F'7&/-F%6#\"\"!F7/-F%
6#F,F./-F%6#F.F./-F%6#\"\"$FA" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "S
o " }{XPPEDIT 18 0 "s[1](x);" "6#-&%\"sG6#\"\"\"6#%\"xG" }{TEXT -1 19 
" can be written as " }{XPPEDIT 18 0 "Sum(b[i]*x^i/i!,i = 0 .. infinit
y);" "6#-%$SumG6$*(&%\"bG6#%\"iG\"\"\")%\"xGF*F+-%*factorialG6#F*!\"\"
/F*;\"\"!%)infinityG" }{TEXT -1 7 " where " }{XPPEDIT 18 0 "b[i] = 2*b
[i-1]-b[i-2];" "6#/&%\"bG6#%\"iG,&*&\"\"#\"\"\"&F%6#,&F'F+\"\"\"!\"\"F
+F+&F%6#,&F'F+\"\"#F0F0" }{TEXT -1 7 ", with " }{XPPEDIT 18 0 "b[0] = \+
0,b[1] = 2,b[2] = 2;" "6%/&%\"bG6#\"\"!F'/&F%6#\"\"\"\"\"#/&F%6#\"\"#
\"\"#" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "b[3] = 3;" "6#/&%\"bG6#\"\"
$\"\"$" }{TEXT -1 1 "." }}}}{MARK "4 0 10" 1 }{VIEWOPTS 1 1 0 1 1 
1803 }