Author(s): G. Sansone; J. Gerretsen
Series: Lectures on the Theory of Functions of a Complex Variable 2
Publisher: Springer
Year: 1968
Language: English
Commentary: OCR'd with ABBYY Finereader (not proofread). The covers is blank so I generated one.
Pages: 700
Geometric Theory
LECTURES ON THE THEORY OE FUNCTIONS OF A COMPLEX VARIABLE II GEOMETRIC THEORY
PREFACE
CONTENTS
Chapter 9 APPLICATIONS OF GENERAL METRICS TO THE THEORY OF FUNCTIONS
9.1. - Topological considerations
9.2 - Conformal mapping
9.3 - Automorphisms of the extended plane
9.4 - Mobius geometry
9.5 - Hyperbolic geometry
9.6 - Elliptic and absolute geometry
9.7 - Blaschke’s theorems
9.8 - Schwarz’s lemma
9.9 - The theorem of Bloch
Chapter 10 CONFORMAL MAPPING OF SIMPLY CONNECTED REGIONS
10.1 - The principle of symmetry
10.2 - Examples of conformal mapping
10.3 - The mapping of a polygon
10.4 - Functions related to the mapping of a square
10.5 - Riemann’s theorem
Chapter 11 UNIVALENT FUNCTIONS
11.1 - Preliminary lemmas
11.2 - Distortion theorems
11.3 - Estimates of coefficients
11.4 - Lowner’s theory
11.5 - Applications of Lowner’s theory
Chapter 12 ANALYTIC FUNCTIONS - RIEMANN SURFACES
12.1- Analytic continuation
12.2 - Analytic functions
12.3 - Algebraic functions
12.4-Riemann surfaces
12.5 - Classification of algebraic Riemann surfaces
12.6 - Uniformization
12.7 - Deformation of paths
Chapter 13 AUTOMORPHIC FUNCTIONS
13.1 - Groups of linear transformations
13.2 - The fundamental domain
13.3 - Fuchsian groups
13.4 - Automorphic functions
13.5 - The Poincare theta series
Chapter 14 THE SCHWARZIAN TRIANGLE FUNCTIONS AND THEIR INVERSES
14.1 - The mapping of a curvilinear polygon
14.2 - The Schwarzian triangles and their associated groups
14.3 - Inverses of the Schwarzian triangle functions
14.4 - Picard’s theorem and related theorems
14.5 - The elliptic modular function
Chapter 15 LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS
15.1 - General theory
15.2 - The theory of Fuchs
15.3 - Bessel functions
15.4 - Legendre’s functions
15.5 - Fuchsian equations
15.6 - Riemann’s equation
Chapter 16 THE HYPERGEOMETRIC DIFFERENTIAL EQUATION
16.1 - The hypergeometric series
16.2 - Hypergeometric polynomials
16.3 - The hypergeometric series as functions of the parameters
16.4 - The fundamental system in the case that the third parameter is an integer
16.5 - Barnes’s contour integrals
16.6 - Conformal mapping
16.7 - Confluent hypergeometric functions
16.8 - Confluent hypergeometric polynomials
INDEX
