Expression 4: "P" Subscript, 4 , Baseline left parenthesis, "x" , right parenthesis equals left parenthesis, "x" minus floor left parenthesis, "x" , right parenthesis , right parenthesis to the 4th power minus 2 left parenthesis, "x" minus floor left parenthesis, "x" , right parenthesis , right parenthesis cubed plus left parenthesis, "x" minus floor left parenthesis, "x" , right parenthesis , right parenthesis squared minus StartFraction, 1 Over 30 , EndFractionP4x=x−floorx4−2x−floorx3+x−floorx2−130
4
Expression 5: "S" Subscript, "N" , Baseline left parenthesis, "x" , right parenthesis equals negative 2 times StartFraction, "m" ! Over left parenthesis, 2 pi , right parenthesis Superscript, "m" , Baseline , EndFraction Start sum from "n" equals 1 to "N" , end sum, StartFraction, cos left parenthesis, 2 pi "n" "x" minus StartNestedFraction, pi NestedOver 2 , EndNestedFraction "m" , right parenthesis Over "n" Superscript, "m" , Baseline , EndFractionSNx=−2·m!2πmN∑n=1cos2πnx−π2mnm