-函数," /> -函数,"/> -functions,"/> Meromorphic Solutions of Finite Order to the Equation <inline-formula><tex-math id="M2"><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-7"><span class="MJXp-msubsup" id="MJXp-Span-8"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-9" style="margin-right: 0.05em;">f</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-10" style="vertical-align: 0.5em;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-11">n</span></span></span><span class="MJXp-mo" id="MJXp-Span-12" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-msubsup" id="MJXp-Span-13"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-14" style="margin-right: 0.05em;">f</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-15" style="vertical-align: 0.5em;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-16">m</span></span></span><span class="MJXp-mo" id="MJXp-Span-17" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-18">z</span><span class="MJXp-mo" id="MJXp-Span-19" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-20">c</span><span class="MJXp-mo" id="MJXp-Span-21" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-22" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-msubsup" id="MJXp-Span-23"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-24" style="margin-right: 0.05em;">e</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-25" style="vertical-align: 0.5em;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-26">A</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-27">z</span><span class="MJXp-mo" id="MJXp-Span-28">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-29">B</span></span></span></span></span><script type="math/tex" id="MathJax-Element-4">f^{n}+f^{m}(z+c)=e^{Az+B}</script></tex-math></inline-formula>

Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 913-920.

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Meromorphic Solutions of Finite Order to the Equation fn+fm(z+c)=eAz+B

Minfeng Chen1,*(),Zongsheng Gao2,Zhibo Huang3   

  1. 1 School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006
    2 LMIB & School of Mathematical Sciences, Beihang University, Beijing 100191
    3 School of Mathematical Sciences, South China Normal University, Guangzhou 510631
  • Received:2020-10-28 Online:2021-08-26 Published:2021-08-09
  • Contact: Minfeng Chen E-mail:chenminfeng198710@126.com
  • Supported by:
    the NSFC(12001117);the NSFC(12001503);the NSFC(11701524);the NSF of Guangdong Province(2018A030313267);the NSF of Guangdong Province(2018A030313508)

Abstract:

In this paper, we study the meromorphic solutions of finite order to the difference equations fn(z)+fm(z+c)=eAz+B (c0) over the complex plane C for integers n,m, and A,B,cC.

Key words: Fermat-type difference equations, Meromorphic solution, Nevanlinna theory, -functions')">Weierstrass's -functions

CLC Number: 

  • O175.29
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