This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever. This text refers to an alternate Paperback edition.
PART I. THE PROCESSES OF ANALYSIS
I Complex Numbers.
II The Theory of Convergence
III Continuous Functions and Uniform Convergence
IV The Theory of Riemann Integration
V The fundamental properties of Analytic Functions; Taylor's, Laurent's,
nod Liouville's Theorems
VI TheTheory of Residues;applieation to the evaluation of Definite lntegrals
VII The expansion of functions in Infinite Series
VIII Asymptotic Expansions and Summable Series .
IX Fourier Series and Trigonometrical Series
X Linear Differential Equations
XI Integral Equations
PART II. THE TRANSCENDENTAL FUNCTIONS
XII The Gamma Funution
XIII The Zeta Function of Riemann
X IV The Hypergeometric Function
XV Legendre Functions
XV I The Confluent Hypergeometric Function.
XVII Bessel Functions
XVIII The Equations of Mathematical Physics
XIX Mathieu Functions
XX Elliptic Functions. General theorems and the Weierstrassian Functions
XXI The Theta Functions
XXII The Jaeobiau Elliptic Functions .
XXIII Ellipsoidal Harmonics and Lame's Equation
LIST OF AUTHORS QUOTED
[NOTE. The decimal system of paragraphing, introduced by Peano, is adopted in this
work. The integral part of the decimal rspresents the ,amber of the chapter and the
fractional parts are arranged in each chapter in order of magnitude. Thus, e.g., on
pp. 187, 188, ξ 9.63.2 precedes ξ 9.7 because 9.63'2 ＜ 9'7.]