[math-fun] something for cos(x) and cosh(x)

the ratio (x/sinh (x)) : (cos(x))^2=(sum(((-1)^n/(2*n)!)*(x/sinh(x))^(2*n)*cosh(2*n*x),n=0..infinity))^2+(sum(((-1)^n/(2*n+1)!)*(x/sinh(x))^(2*n+1)*cosh((2*n+1)*x),n=0..infinity))^2; and with x=i*x (cosh(x))^2=(sum(((-1)^n/(2*n)!)*(x/sin(x))^(2*n)*cos(2*n*x),n=0..infinity))^2+(sum(((-1)^n/(2*n+1)!)*(x/sin(x))^(2*n+1)*cos((2*n+1)*x),n=0..infinity))^2; FME...