{VERSION 3 0 "SGI MIPS UNIX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{PSTYLE " Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {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 " 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 }