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读者对象为从事复分析研究的学者及从事数学,物理,化学,工程工作的工程师.
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| 內容簡介： |
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陈宗煊编著的《复域差分与差分方程英文版精》介绍了，This book mainly contains the basic theory of complex differences, difference equa-tions and new results on this research field in recent years.Chapters 1-4 mainly introduce basic properties of complex differences and differ-ence polynomials. Chapters 5 to 9 are devoted to analytic properties of difference equa-tions. Chapter 10 deals with the value distribution of q-differences and q-differenceequations. Chapter 11 is concerned with the uniqueness problem.
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| 目錄：
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Preface
List of Symbols
Chapter 1 Basic Properties of Complex Differences
1.1 Preliminaries
1.2 Difference Analogue of the Lemma on the Logarithmic Derivative
1.3 Estimations of Nr, fz + η
1.4 Estimations of Tr, fz + η
1.5 Difference Analogue of the Clunie Lemma
1.6 Difference Analogue of the Mohon''ko Lemma
1.7 Difference Analogue of the Second Main Theorem
1.8 Characteristic Functions of △nf
Chapter 2 Relationships Between Meromorphic Functions and Differences
2.1 Relationships of fz and △nfz
2.2 Fixed Points of fz, fz + c and △fz
Chapter 3 Differences of Meromorphic Functions with Small Growth
3.1 Divided Differences of Entire Functions of order 1
3.2 Differences of Entire Functions of order≤ 1
3.3 Differences of Meromorphic Functions
3.4 Second Differences of Meromorphic Functions with Small Growth
Chapter 4 Properties of Difference Polynomials
4.1 Difference Analogues of fznf''z
4.2 Difference Analogues of f''z - afz
4.3 Difference Analogue of the Tumura-Clunie Type Theorems
Chapter 5 Linear First Order Difference Equations
5.1 Equations Concerning Gamma Function
5.2 General Linear First Order Difference Equations
5.3 Differences of Solutions for Difference Equations, and Differences of rz
Chapter 6 Linear Higher Order Difference Equations
6.1 Difference Equations with Rational Coefficients
6.2 Difference Equations with Transcendental Coefficients
Chapter 7 Basic Properties of Nonlinear Difference Equations
7.1 Basic Properties Concerning Order Number
7.2 Properties of Meromorphic Solutions
Chapter 8 Difference Riccati Equations
8.1 Pielou Logistic Equation
8.2 Difference Riccati Equations
8.3 A Family of Solutions for Difference Riccati Equations
Chapter 9 Difference Painleve Equations
9.1 Classified of Second Difference Equations
9.2 Difference PainleveⅡ Equations
9.3 Difference Painleve Ⅰ Equations
9.4 Difference Painleve Ⅲ Equations
Chapter 10 Complex q-Differences and q-Difference Equations
10.1 Properties of q-Differences
10.2 Linear q-Difference Equations
10.3 Non-Linear q-Difference Equations
10.4 q-Difference Riceati equations
Chapter 11 Unicity of Meromorphic Functions Concerning Their Differences and Shifts
11.1 Meromorphic Functions fz that Share Values with fz + c
11.2 Meromorphic Functions fz that Share Values with △fz
11.3 Meromorphic Functions fz that Share Values with △fz and△2z
11.4 Meromorphic Functions fz that Share Values with △nfz
Bibliography
Index
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