高阶复微分方程的解.pdf

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1、学校代码：10663学号：4201210000322贵贵贵州州州师师师范范范大大大学学学硕硕硕士士士学学学位位位论论论文文文高高高阶阶阶复复复微微微分分分方方方程程程的的的解解解Solutionsofhigherordercomplexdifferentialequations专业名称：基础数学专业代码：070101研究方向：函数论申请人姓名：易善峰导师姓名：伍鹏程(教授)二零一五年四月五日目录摘摘摘要要要··································································

2、·························IAbstract···························································································II1引引引言言言与与与主主主要要要结结结果果果················································································11.1国内外研究现状及研究意义··························

3、································11.2本文相关定义及记号···································································21.3主要结果··················································································42复复复平平平面面面高高高阶阶阶微微微分分分方方方程程程解解解的的的[p,q]增增增长长长级级级····················

4、································62.1引言与结果···············································································62.2引理························································································72.3定理1的证明···············································

5、······························82.4定理2的证明·············································································93单单单位位位圆圆圆上上上高高高阶阶阶齐齐齐次次次线线线性性性微微微分分分方方方程程程解解解的的的[p,q]增增增长长长级级级·····································113.1引言与结果···········································

6、····································113.2引理························································································113.3定理3的证明·············································································123.4定理4的证明·········································

7、····································124总总总结结结和和和展展展望望望······················································································134.1总结························································································134.2展望·····························

8、···························································13参参参考考考文文文献献献······························