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In this exampl e we compare convergence of Fourier sine and cosine series." }}{PARA 0 "" 0 "" {TEXT -1 138 " The function, f(x)=2x, 0 " 0 "" {MPLTEXT 1 0 21 "f := x -> 2*x; L:=10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"x G6\"6$%)operatorG%&arrowGF(,$9$\"\"#F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "a := k -> 2/L*int(f(x)*cos(k*Pi*x/L),x=0..L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGf*6#%\"kG6\"6$%)operatorG%&arrowGF(,$*&-%$intG6$* &-%\"fG6#%\"xG\"\"\"-%$cosG6#*&*(9$F6%#PiGF6F5F6F6%\"LG!\"\"F6/F5;\"\" !F>F6F>F?\"\"#F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "Note that the integral has not been evaluated.\nNext we can calculate some part ial sums." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "cs := (x,n) -> a(0)/2 + sum(a(k)*cos(k*Pi*x/L),k=1..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#csGf*6$%\"xG%\"nG6\"6$%)operatorG%&arrowGF),&-%\"aG6 #\"\"!#\"\"\"\"\"#-%$sumG6$*&-F/6#%\"kGF3-%$cosG6#*&*(F;F3%#PiGF39$F3F 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