Book:Edmund Taylor Whittaker/A course of modern analysis/Third edition

Edmund Taylor Whittaker and George Neville Watson: A course of modern analysis

Published $1920$, Cambridge University Press.

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Contents

PART I. THE PROCESSES OF ANALYSIS

Chapter I Complex Numbers

Chapter II The Theory of Convergence

Chapter III Continuous Functions and Uniform Convergence

Chapter IV The Theory of Riemann Integration

Chapter V The fundamental properties of Analytic Functions; Taylor's, Laurent's, and Liouville's Theorems

Chapter VI The Theory of Residues; application to the evaluation of Definite Integrals

Chapter VII The expansion of functions in Infinite Series

Chapter VIII Asymptotic Expansions and Summable Series

Chapter IX Fourier Series and Trigonometrical Series

Chapter X Linear Differential Equations

Chapter XI Integral Equations

PART II. THE TRANSCENDENTAL FUNCTIONS

Chapter XII The Gamma Function

$\S 12 \cdot 1$

$\S 12 \cdot 1$

$\S 12 \cdot 11$

$\S 12\cdot 12$

Chapter XIII The Zeta Function of Riemann

Chapter XIV The Hypergeometric Function

Chapter XV Legendre Functions

Chapter XVI The Confluent Hypergeometric Function

Chapter XVII Bessel Functions

Chapter XVIII The Equations of Mathematical Physics

Chapter XIX Mathieu Functions

Chapter XX Elliptic Functions, General theorems of the Weierstrassian Functions

Chapter XXI The Theta Functions

Chapter XXII The Jacobian Elliptic Functions

Chapter XXIII Ellipsoidal Harmonics and Lamé's Equation

APPENDIX

LIST OF AUTHORS QUOTED

GENERAL INDEX