On the Growth of Logarithmic Difference of Meromorphic Functions and a Wiman–Valiron Estimate

Yik Man Chiang; Shaoji Feng

doi:10.1007/s00365-016-9324-8

On the Growth of Logarithmic Difference of Meromorphic Functions and a Wiman–Valiron Estimate

Yik Man Chiang^*, Shaoji Feng

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal Article › peer-review

8 Citations (Scopus)

Abstract

This 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 polynomial coefficients for linear difference equations.

Original language	English
Pages (from-to)	313-326
Number of pages	14
Journal	Constructive Approximation
Volume	44
Issue number	3
DOIs	https://doi.org/10.1007/s00365-016-9324-8
Publication status	Published - 1 Dec 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Keywords

Difference Wiman–Valiron estimates
Finite order meromorphic functions
Linear difference equations

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10.1007/s00365-016-9324-8

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abstract = "This 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 polynomial coefficients for linear difference equations.",

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AU - Feng, Shaoji

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N2 - This 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 polynomial coefficients for linear difference equations.

AB - This 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 polynomial coefficients for linear difference equations.

KW - Difference Wiman–Valiron estimates

KW - Finite order meromorphic functions

KW - Linear difference equations

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JO - Constructive Approximation

JF - Constructive Approximation

IS - 3

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On the Growth of Logarithmic Difference of Meromorphic Functions and a Wiman–Valiron Estimate

Abstract

Bibliographical note

Keywords

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