Relative growth order of entire functions (Q749702)

The author proposes a generalization from the order of an entire function to an order of one function with respect to another. Let F denote the maximum modulus of f. Then \(\rho\) (f) (relative to g) is defined as the infimum of positive numbers \(\mu\) for which \(F(r)<G(r^{\mu})\) for all r greater than some positive \(r_ 0\). The author investigates the behavior of this order with respect to elementary operations, the Nevanlinna characteristic, and Taylor coefficients.