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

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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 |

278 | |

### Other editions - View all

### Common terms and phrases

absolute convergence acquire aggregate algebraic equation algebraic functions canonical form characteristic equation coefficients combinations common factor complex variables consider constants converges absolutely denote different from zero domain round double integral double series double theta-functions dw dw dzdz essential singularities expression f and g field of variation finite values function f(z function of z given hence immediate vicinity independent functions independent variables infinite infinitesimal periods infinity integer invariant centres Jacobian level places level values limited linear lineo-linear transformation manifestly multiple odd functions parallelogram period-pairs plane pole polynomial positive integer power-series preceding quadratic frontier quadruply periodic functions quotient range rational function real variables regard regular function relations representation represented result roots satisfied shews Similarly single variable theorem theory of functions triply periodic functions unessential uniform analytic function uniform function vanish identically Weierstrass z and z z-plane zero-place