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Some topics in complex analysis
Some Topics in Complex Analysis.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford, New York,
Pergamon Press
[1966]
|
| Edición: | [1st ed.]. |
| Colección: | International series of monographs in pure and applied mathematics ;
v. 86. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 2.1 The Periods of an Integral2.2 The Function sn u; 2.3 The Constants K and K; 2.4 The Functions cn u, dn u; 2.5 The Addition Theorems; 2.6 Periodicity; 2.7 Expansions in Powers of u; 2.8 Identities and Duplication Formulae; 2.9 Jacobi's ""Imaginary"" Transformation; 2.10 The Jacobian Functions for Values Connected with the Periods; 2.11 Applications of the Method of Comparison to Jacobian Functions; 2.12 The Relation Between Weierstrassian and Jacobian E.F.; 2.13 Elliptic Integrals; 2.14 The Functions E(u) and Z(u); Examples 2; CHAPTER 3. CONFORMAL TRANSFORMATION
- 3.1 Ratio of Two Quadratics3.2 Generalized Joukowski Transformations; 3.3 Boundary a Closed Polygon; 3.4 Schwarz-Christoffel Transformation; 3.5 Transformations Involving Elliptic Functions; 3.6 Note on Transformations Involving E.F.; 3.7 Schwarz's Lemma; 3.8 Extension of Schwarz's Lemma; 3.9 An Estimate of the Derivative of a Bounded Function; 3.10 Functions with a Positive Real Part; 3.11 Schwarz's Symmetry Principle; 3.12; Examples 3; CHAPTER 4. SCHLICHT FUNCTIONS; 4.1; 4.2 Definition; 4.3 Some Distortion Theorems; 4.4; 4.5 Koebe's Distortion Theorems; 4.6 Bieberbach's Inequality
- Examples 4CHAPTER 5. THE MAXIMUM-MODULUS PRINCIPLE; 5.1 The Maximum-Modulus Theorem; 5.2 The Phragm�en-Lindel�of Extension; 5.3 Deductions from the Maximum-Modulus Principle; 5.4; 5.5; 5.6; Examples 5; CHAPTER 6. INTEGRAL FUNCTIONS; 6.1 Definition and Preliminaries; 6.2 Weierstrass's Primary Factors; 6.3 The Order of an I.F.; 6.4 Jensen's Theorem; 6.5 The Function n(r) for an I.F.; 6.6 Canonical Products and Genus of an I.F.; 6.7 Hadamard's Theorem on I.F. of Finite Order; 6.8 The Coefficients in the Expansion of an I.F. of Finite Order; Examples 6; CHAPTER 7. EXPANSIONS IN INFINITE SERIES