ADVANTAGE has been taken of the prearation of the fourth edition of this work to add a few additional referens and to make a number of corrections of minor errors.

Our thanks are bue to a number of our readers for pointing out errors and misprints,and in particular we are grateful to Mr E.T.Copson,Lecturer in mathematics in the University Edinburgh,for the trouble which he has taken in supplying us with a somewhat lenthy list.

PART I. THE PROCESSES OF ANALYSIS

CHAPTER

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 ; Tay]or's, Laurent's,and Liouville's Theorems

VI  TheTheory of Residues; application to the evaluation of Definite Integrals

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 Function

XIII The Zeta Function of Riemann

XIV The I'lypergeometric Function

XV Legendre Functions

XVI The Coufluent Hypergeometric Function

XVII Bessel Functions

XVIII The Equations of Mathematical Physics

XIX  Mathieu Functions

XX  Elliptiv Functions. General theorems and the Weierstrassian Functions

XXI  The Theta Functions

XXII The Jacobian Elliptic Functions .

XXIII Ellipsoial Harmonics and Lamd's Equation

APPENDIX

LIST OF AUTHORS QUOTED

GENERAL INDEX