Page:A Course of Modern Analysis - 3rd edition - 1920.pdf/13

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Contents
Part I. The Processes of Analysis
Chapter Page
I Complex Numbers 3
II The Theory of Convergence 11
III Continuous Functions and Uniform Convergence 41
IV The Theory of Riemann Integration 61
V The fundamental properties of Analytic Functions; Taylor's, Laurent's, and Lionville's Theorems 82
VI The Theory of Residues; application to the evaluation of Definite Integrals 111
VII The expansion of functions in Infinite Series 125
VIII Asymptotic Expansions and Summable Series 150
IX Fourier Series and Trigonometric Series 160
X Linear Differential Equations 194
XI Integral Expansion 211
Part II. The Transcendental Functions
XII The Gamma Function 235
XIII The Zeta Function of Riemann 265
XIV The Hypergeometric Function 281
XV Legendre Functions 302
XVI The Confluent Hypergeometric Function 337
XVII Bessel Functions 355
XVIII The Equations of Mathematical Physics 386
XIX Mathieu Functions 404
XX Elliptic Functions. General theorems and the Weierstraussian Functions 429
XXI The Theta Functions 462
XXII The Jacobian Elliptic Functions 491
XXIII Ellipsoidal Harmonics and Lamé's Equation 536
Appendix 579
List of Authors Quoted 591
General Index 595


[Note. The decimal system of paragraphing, introduced by Peano, is adopted in this work. The integral part of the decimal represents the number of the chapter and the fractional parts are arranged in each chapter in order of magnitude. Thus, e.g., on pp. 187, 188, § 9·632 precedes § 9·7 because 9·632 < 9·7.]