Functions of a Complex Variable单复变函数

Developed from a highly successful series of lectures given at Yale University, this volume has a reputation as one of the best texts in its field. A thorough treatment of the fundamental elements, concepts,and theorems pertaining to the function of a complex variable, it offers a complete study, suitable for advanced mathematics students,physicists, and advanced engineers.
Students of applied mathematics will particularly value the full exposi-tion of the theory of linear differential equations, especially in regard to the functions of Legendre, Laplace, Bessel, and Lame. Three chapters are devoted to elliptic functions, explaining both their intrinsic value and their role as splendid applications of function theory. Rigorous and detailed in its treatment, this text features carefully selected and com-pletely worked-out problems that illustrate each topic.

CHAPTER I ARITHMETICAL OPERATIONS
ARTICLES
CHAPTER II REAL TERM SERIES
POSITIVE TERM SERIES
CHAPTER III SERIES WITH COMPLEX TERMS
ARTICLES
POWER SERIES
CHAPTER IV THE ELEMENTARY FUNCTIONS
EXPONENTIAL FUNCTION
CIRCULAR FUNCTIONS
ARTICLES
OTHER FUNCTIONS
CHAPTER V RELA VARIABLES
INTEGRATION
CHAPTER VI DEFFERENTIATION AND INTEGRATION
ARTICLES
INTEGRATION
FUNCTIONS DEFINED BY SERIES
CHAPTER VII ANALYTIC FUNCTIONS
CHAPTER VIII INFINITE PRODUCTS
ARTICLES
CHAPTER IX B AND F FUNCTIONS,ASYMPTOTIC EXPANSIONS
ASYMPTOTIC EXPANSIONS
CHAPTER X FUNCTIONS OF WEIERSTRASS
ARTICLES
CHAPTER XI FUNCTICON AND JACOBI
CHAPTER XII THETA FUNCTIONS
CHATPER XIII LINEAR DEFFERENTIAL EQUATIONS
CHAPTER XIV FUNCTIONS OF LEGENDRE AND LAPLACE
LAPLACE'S FUNCTIONS
ARTICTES
CHAPTER XV BESSEL AND LAME FUNCTIONS
NOTE