{VERSION 5 0 "IBM INTEL LINUX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {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 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 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "#This program check s whether the period of the summation function is ln(5) and how period ic the function is. This particular version corresponds to the 5-seri es. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "read \"values_5.m\" ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 164 "#This is the summation function we've used previou sly. You can easily change what range of sequences \"j\" you sum over , but this will affect the range of the graph." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 " summation5:= x -> (x^((log(25/3))/log(5)))*sum('(exp(-(El5[j])*x))*((d n5[j])^2)','j'=1..512);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+summatio n5Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&)9$*&-%$logG6##\"#D\"\"$\"\"\" -F16#\"\"&!\"\"F6-%$sumG6$.*&-%$expG6#,$*&&%$El5G6#%\"jGF6F.F6F:F6)&%$ dn5GFG\"\"#F6/.FH;F6\"$7&F6F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "#Now we shift the function over by ln(5). Since it' s in a logarithmic scale, it requires dividing by 5 rather than subtra cting." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "oneshiftover:= x -> ((x/5)^((log(25/3))/ log(5)))*sum('(exp(-(El5[j])*(x/5)))*((dn5[j])^2)','j'=1..512);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%-oneshiftoverGf*6#%\"xG6\"6$%)operat orG%&arrowGF(*&),$*\"\"\"\"\"&F19$F1F1*&-%$logG6##\"#D\"\"$F1-F66#F2 !\"\"F1-%$sumG6$.*&-%$expG6#,$*F1F2F1*&&%$El5G6#%\"jGF1F3F1F1F=F1)&% $dn5GFL\"\"#F1/.FM;F1\"$7&F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "#Now we plot the shifted function to see how it looks." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 " plot([log(1/x),oneshiftover(x),x=10^(-8)..3/1000], style=point, numpoi nts=10000);" }}{PARA 13 "" 1 "" {GLPLOT2D 375 375 375 {PLOTDATA 2 "6&- %'CURVESG6$7d^bm7$$\"3sO_Ru!o?%=!#;$\"3yjF??OLzL!#>7$$\"3gGdMv&4Px\"F* $\"3
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