Suppose that \(f\) is meromorphic on the plane, is never zero on the plane, and that \[ \lim _{z\to \infty }|f(z)|=0. \] Show that \(f\) is the inverse of a polynomial.
Question
Math 6210 • Real Analysis
2002 • Question 10
Question
2002 • Question 10
Suppose that \(f\) is meromorphic on the plane, is never zero on the plane, and that \[ \lim _{z\to \infty }|f(z)|=0. \] Show that \(f\) is the inverse of a polynomial.