Expression 4: "a" left parenthesis, "n" , right parenthesis equals StartFraction, left parenthesis, negative 1 , right parenthesis Superscript, left parenthesis, "n" plus 1 , right parenthesis , Baseline minus 1 Over pi left parenthesis, 1 minus "n" squared , right parenthesis , EndFractionan=−1n+1−1π1−n2
4
Expression 5: "a" left parenthesis, "z" , right parenthesis cosine left parenthesis, StartFraction, "z" pi "x" Over 2 , EndFraction , right parenthesisazcoszπx2
5
Expression 6: 1 half sine left parenthesis, StartFraction, pi "x" Over 2 , EndFraction , right parenthesis12sinπx2
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Expression 7: negative StartFraction, 1 Over pi , EndFraction plus 1 half sine left parenthesis, StartFraction, pi "x" Over 2 , EndFraction , right parenthesis plus Start sum from "n" equals 2 to "N" , end sum, left parenthesis, "a" left parenthesis, "n" , right parenthesis cos left parenthesis, StartFraction, pi "n" "x" Over 2 , EndFraction , right parenthesis , right parenthesis−1π+12sinπx2+N∑n=2ancosπnx2