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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
[2](x) = Sum(b[i]*x^i/i!,i = 0 .. infinity);" "6#/-&%\"sG6#\"\"#6#%\"x
G-%$SumG6$*(&%\"bG6#%\"iG\"\"\")F*F2F3-%*factorialG6#F2!\"\"/F2;\"\"!%
)infinityG" }{TEXT -1 8 ", where " }{XPPEDIT 18 0 "b[i] = b[i-1]+b[i-2
];" "6#/&%\"bG6#%\"iG,&&F%6#,&F'\"\"\"\"\"\"!\"\"F,&F%6#,&F'F,\"\"#F.F
," }{TEXT -1 6 " with " }{XPPEDIT 18 0 "b[0] = 0;" "6#/&%\"bG6#\"\"!F'
" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "b[1] = 1;" "6#/&%\"bG6#\"\"\"\"
\"\"" }{TEXT -1 9 ".  These " }{XPPEDIT 18 0 "b[i];" "6#&%\"bG6#%\"iG
" }{TEXT -1 118 " are the Fibonacci numbers \\cite\{Abramowitz\}.  \\L
abel\{defn:Fib\}  Converting this to a poly-exponential function gives
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "s[2] := b(x) = b(x-1) \+
+ b(x-2), b, x, [b(0) = 0, b(1) = 1];" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>&%\"sG6#\"\"#6&/-%\"bG6#%\"xG,&-F+6#,&F-\"\"\"!\"\"F2F2-F+6#,&F-F2
!\"#F2F2F+F-7$/-F+6#\"\"!F</-F+6#F2F2" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "convert_pe(s[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$
,&*&-%%sqrtG6#\"\"&\"\"\"-%$expG6#*&%\"xG\"\"\",&#F/\"\"#F/*$F%F)#!\"
\"F2F/F/#F5F(*&F%F)-F+6#*&F.F),&F1F/F3F1F/F/#F/F(F." }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 77 "So this can be written as a poly-exponential fu
nction, as demonstrated above." }}}}{MARK "4 0 0" 0 }{VIEWOPTS 1 1 0 
1 1 1803 }