On the growth of logarithmic difference of meromorphic functions and a Wiman-Valiron estimate

Abstract

The paper gives a precise asymptotic relation between higher order logarithmic difference and logarithmic derivatives for meromorphic functions with order strictly less then one. This allows us to formulate a useful Wiman-Valiron type estimate for logarithmic difference of meromorphic functions of small order. We then apply this estimate to prove a classical analogue of Valiron about entire solutions to linear differential equations with polynomials coefficients for linear difference equations.

Corrected further typos. Revised the error term estimates in Theorem 5.2. Added a dedication, Constructive Approximations (published online 21 January, 2016)

Cited by in corpus (3)

• Nevanlinna theory for Jackson difference operators and entire solutions of q-difference equations
• Wiman-Valiron theory for a polynomial series based on the Wilson operator
• Binomial series and complex difference equations