{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 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 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 -1 238 "This example will demonstrate that proce ss of multisectioning can be used where the recurrence has symbolic va lues rather than simply numeric ones. Consider the \{\\em Chebyshev T polynomials\}'', as polynomials in t, with the recurrence " } {XPPEDIT 18 0 "T[n] = 2*t*T[n-1]-T[n-2];" "6#/&%\"TG6#%\"nG,&*(\"\"#\" \"\"%\"tGF+&F%6#,&F'F+\"\"\"!\"\"F+F+&F%6#,&F'F+\"\"#F1F1" }{TEXT -1 26 " with initial polynomials " }{XPPEDIT 18 0 "T[0] = 1;" "6#/&%\"TG6 #\"\"!\"\"\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "T[1] = t;" "6#/&%\"T G6#\"\"\"%\"tG" }{TEXT -1 86 " \\cite\{Abramowitz\}. Consider multise ctioning this by 5 at 1, to get a recurrence for " }{XPPEDIT 18 0 "T[1 ];" "6#&%\"TG6#\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "T[6];" "6#&%\" TG6#\"\"'" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "T[11];" "6#&%\"TG6#\"#6" } {TEXT -1 2 ", " }{XPPEDIT 18 0 "T[16];" "6#&%\"TG6#\"#;" }{TEXT -1 5 " , ..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "egf := f(x) = 2*t* f(x-1)-f(x-2),f,x,[f(0)=1, f(1)=t];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$egfG6&/-%\"fG6#%\"xG,&*&%\"tG\"\"\"-F(6#,&F*F.!\"\"F.F.\"\"#-F(6#, &F*F.!\"#F.F2F(F*7$/-F(6#\"\"!F./-F(6#F.F-" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 18 "egf/ms(egf,5,1);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6&/-%\"fG6#%\"xG,&-F%6#,&F'\"\"\"!#5F,!\"\"*&,(*$)%\"tG\"\"&\"\"\"\"# K*$)F3\"\"$F5!#SF3\"#5F,-F%6#,&F'F,!\"&F,F,F,F%F'7,/-F%6#\"\"!FD/-F%6# F,F3/-F%6#\"\"#FD/-F%6#F9FD/-F%6#\"\"%FD/-F%6#F4FD/-F%6#\"\"',**&F3F5, (*&F3F5,(*&F3F5,&*&F3F,,&*$)F3FKF5FKF.F,F,FKF3F.F,FKF]o!\"#F,F,F,FKF[o F_oF3F,F,FKFinF_oF]oFKF.F,/-F%6#\"\"(FD/-F%6#\"\")FD/-F%6#\"\"*FD" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "expand([%]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&/-%\"fG6#%\"xG,*-F&6#,&F(\"\"\"!#5F-!\"\"*&-F&6# ,&F(F-!\"&F-F-)%\"tG\"\"&\"\"\"\"#K*&F1F8)F6\"\"\$F8!#S*&F1F8F6F-\"#5F& F(7,/-F&6#\"\"!FD/-F&6#F-F6/-F&6#\"\"#FD/-F&6#F