Did you read Othello my dear ?? a recurrence for functions a(n+1)=2^(n+3/2)*sqrt(1-sqrt(1-2^(-2*n-2)*a(n)^2)) ; for : a(0)=sqrt(2-2/sqrt(1+x^2)) ; n -------- infinity ; a(n) ------- atan(x) ; for : a(0)=sqrt(2-2*x) ; n -------- infinity ; a(n) ------- acos(x) ; for : a(0)=sqrt(2-2*sqrt(1-x^2)) ; n -------- infinity ; a(n) ------- asin(x) ; for : a(0)=sqrt(2-2*x/sqrt(1+x^2)) ; n -------- infinity ; a(n) ------- acot(x) ; The results are in absolute values FME...