Expression 3: "f" left parenthesis, "y" , "x" , right parenthesis equals left brace, "x" less than or equal to 0 : arctan left parenthesis, StartFraction, "y" Over "x" , EndFraction , right parenthesis plus pi , arctan left parenthesis, StartFraction, "y" Over "x" , EndFraction , right parenthesis , right bracefy,x=x≤0:arctanyx+π,arctanyx
3
Expression 4: 0 greater than or equal to Start product from "n" equals 1 to "m" , end product, left parenthesis, StartRoot, left parenthesis, "x" minus "R" left parenthesis, StartFraction, 2 pi "n" Over "m" , EndFraction , right parenthesis cos StartFraction, 2 pi "n" Over "m" , EndFraction , right parenthesis squared plus left parenthesis, "y" minus "R" left parenthesis, StartFraction, 2 pi "n" Over "m" , EndFraction , right parenthesis sin StartFraction, 2 pi "n" Over "m" , EndFraction , right parenthesis squared , EndRoot minus left parenthesis, "R" left parenthesis, "f" left parenthesis, "y" minus "R" left parenthesis, StartFraction, 2 pi "n" Over "m" , EndFraction , right parenthesis sin StartFraction, 2 pi "n" Over "m" , EndFraction , "x" minus "R" left parenthesis, StartFraction, 2 pi "n" Over "m" , EndFraction , right parenthesis cos StartFraction, 2 pi "n" Over "m" , EndFraction , right parenthesis plus 2 left parenthesis, StartFraction, 2 pi "n" Over "m" , EndFraction , right parenthesis , right parenthesis , right parenthesis , right parenthesis0≥m∏n=1x−R2πnmcos2πnm2+y−R2πnmsin2πnm2−Rfy−R2πnmsin2πnm,x−R2πnmcos2πnm+22πnm