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