Lectures Introductory to the Theory of Functions of Two Complex Variables: Delivered to the University of Calcutta During January and February 1913

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CUP Archive, 1914 - Functions - 281 pages
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Contents

CHAPTER I
1
CHAPTER II
25
When the axes of real quantities are conserved
35
Invariants and covariants of quadratic frontiers
39
Introduction of homogeneous variables and umbral forms use of Lies theory of continuous groups
40
Simple examples of invariants and covariants
41
The infinitesimal transformations
43
Number of algebraically independent integrals
46
A theorem expressing by means of a double integral any number of terms in the expansion of a regular function
67
Domiuant functions associated with a regular function
70
Absolute convergence of a double powerseries
72
The investigations of Picard Borel and others in regard to the same property for a regular function of one variable
77
Extension of Picards theorem concerning functions of one variable
78
Weierstrasss process of analytical continuation of a function the region of continuity
81
Singularities unessential essential of uniform functions
82
Two kinds of unessential singularity for a uniform function of two variables discriminated in name by pole and the other type of unessential singulari...
84

Determination of the four invariants
48
Contragredient variables
49
Suggested canonical form of equations for a quadratic frontier
50
Periodic lineolinear transformations
52
CHAPTER III
57
Uniform multiform for functions with an example
58
Continuous analytic regular integral transcendental algebraic mero morphic for functions
59
Property of function establishing its regularity
61
Upper limits for the moduli of derivatives of a regular function some double integrals
66
UNIFORM FUNCTIONS IN RESTRICTED DOMAINS
92
CHAPTER V
124
Weierstrasss theorem as adumbrated on functions having essential
130
CHAPTER VI
152
CHAPTER VII
198
CHAPTER VIII
213
Algebraic relations between three uniform quadruply periodic functions
260
Index
278

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