%0 Journal Article
%T 某类复微分&#8211;差分多项式的唯一性<br>Uniqueness of Certain Classes of Complex Differential-Difference Polynomials
%A 魏立航
%A 姚欣君
%J Pure Mathematics
%P 180-189
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.151021
%X 设<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>g</mi><mrow><mo>(</mo>
   <mi>z</mi>
  <mo>)</mo></mrow></mrow>
</math>

是一个有限级超越亚纯函数&#65292;<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>c</mi><mo>&#x2208;</mo><mi>C</mi></mrow>
</math>

是一个非零常数。对于任意的<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>n</mi><mo>&#x2208;</mo><msup>
   <mi>N</mi>
   <mo>+</mo>
  </msup>
  </mrow>
</math>

&#65292;假设<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mover accent='true'>
   <mi>L</mi>
   <mo>&#x02DC;</mo>
  </mover>
  <mrow><mo>(</mo>
   <mrow>
    <mi>z</mi><mo>,</mo><mi>g</mi></mrow>
  <mo>)</mo></mrow></mrow>
</math>

是下面的微分差分多项式的形式&#65306;<img src=\"https://html.hanspub.org/file/1252703-rId18.svg?20250205114228\" >&#65292;其中&#65292;<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>n</mi><mo>&#x2265;</mo><mn>0</mn><mo>,</mo><mi>m</mi><mo>&#x2265;</mo><mn>1</mn><mo>,</mo><msub>
   <mi>b</mi>
   <mi>i</mi>
  </msub>
  <mo>,</mo><msub>
   <mi>d</mi>
   <mi>k</mi>
  </msub>
  <mo>,</mo><msub>
   <mi>l</mi>
   <mi>j</mi>
  </msub>
  </mrow>
</math>

不是全为零的复数。在本篇文章中&#65292;主要研究了<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mover accent='true'>
   <mi>L</mi>
   <mo>&#x02DC;</mo>
  </mover>
  <mrow><mo>(</mo>
   <mrow>
    <mi>z</mi><mo>,</mo><mi>g</mi></mrow>
  <mo>)</mo></mrow></mrow>
</math>

的唯一性问题。<br>Let <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>g</mi><mrow><mo>(</mo>
   <mi>z</mi>
  <mo>)</mo></mrow></mrow>
</math>

 be a transcendental meromorphic function of finite order and <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>c</mi><mo>&#x2208;</mo><mi>C</mi></mrow>
</math>

 be a nonzero constant. For any <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>n</mi><mo>&#x2208;</mo><msup>
   <mi>N</mi>
   <mo>+</mo>
  </msup>
  </mrow>
</math>

, suppose that <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mover accent='true'>
   <mi>L</mi>
   <mo>&#x02DC;</mo>
  </mover>
  <mrow><mo>(</mo>
   <mrow>
    <mi>z</mi><mo>,</mo><mi>g</mi></mrow>
  <mo>)</mo></mrow></mrow>
</math>

 is a differential-difference polynomial of the form <img src=\"https://html.hanspub.org/file/1252703-rId18.svg?20250205114228\" >, where <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>n</mi><mo>&#x2265;</mo><mn>0</mn><mo>,</mo><mi>m</mi><mo>&#x2265;</mo><mn>1</mn><mo>,</mo><msub>
   <mi>b</mi>
   <mi>i</mi>
  </msub>
  <mo>,</mo><msub>
   <mi>d</mi>
   <mi>k</mi>
  </msub>
  <mo>,</mo><msub>
   <mi>l</mi>
   <mi>j</mi>
%K 微分差分方程&#65292
%K Borel例外值&#65292
%K 唯一性<br>Differential-Difference Equation
%K Borel Exceptional Values
%K Uniqueness
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=106258