{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 [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 }