A functional equation and Jacobian elliptic functions (Q1271582)

This paper is concerned with the functional equation \(\frac{f(x+y)}{f(x-y)}=\frac{g(x)+g(y)}{g(x)-g(y)}\) where \(f\) and \(g\) are meromorphic functions. It is shown that the general solution can be given in terms of Jacobian elliptic functions, or trigonometric or linear functions obtained thereof as limiting cases. Special consideration is given to solutions which are real on the real axis.