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arXiv · 1309.4211

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

Yik-Man Chiang·Shao-Ji Feng
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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.

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Yik-Man Chiang, Shao-Ji Feng. 2016-04-29. On the growth of logarithmic difference of meromorphic functions and a Wiman-Valiron estimate. https://doi.org/10.1007/s00365-016-9324-8

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