[math-fun] Identity for Pi

Hello, Here is a identity that j found, with a ratio between cosine and hyperbolic cosine. Pi=2*mu*x+2*sum((1/n)*(cos(mu*x)/cosh(alpha*x))^n*cosh(mu*n*x)*sin(alpha*n*x),n=1..infinity); This identity seems true for the following conditions: mu = alpha  and  x in [1/mu , 2/mu] The value of x, for which this identity is the most convergent is close to : x = (1.5)*(1/mu) The values of x, verifying the identity seem to form a parable whose vertex corresponds to (1/2) * (1 / mu), which I found curious0 Why ???