AMS Chelsea Publishing 1949; 396 pp; hardcover Volume: 334 ISBN10: 0821826492 ISBN13: 9780821826492 List Price: US$54 Member Price: US$48.60 Order Code: CHEL/334.H
 From the Preface by J. E. Littlewood: "All [Hardy's] books gave him some degree of pleasure, but this one, his last, was his favourite. When embarking on it he told me that he believed in its value (as well he might), and also that he looked forward to the task with enthusiasm. He had actually given lectures on the subject at intervals ever since his return to Cambridge in 1931, and he had at one time or another lectured on everything in the book except Chapter XIII [The EulerMacLaurin sum formula] ... [I]n the early years of the century the subject [Divergent Series], while in no way mystical or unrigorous, was regarded as sensational, and about the present title, now colourless, there hung an aroma of paradox and audacity." Reviews Review of original edition ... "This is an inspiring textbook for students who know the theory of functions of real and complex variables and wish further knowledge of mathematical analysis. There are no problems displayed and labelled "problems," but one who follows all of the arguments and calculations of the text will find use for his ingenuity and pencil. The book deals with interesting and important problems and topics in many fields of mathematical analysis, to an extent very much greater than that indicated by the titles of the chapters. It is, of course, an indispensable handbook for those interested in divergent series. It assembles a considerable part of the theory of divergent series, which has previously existed only in periodical literature. Hardy has greatly simplified and improved many theories, theorems and proofs. In addition, numerous acknowledgements show that the book incorporates many previously unpublished results and improvements of old results, communicated to Hardy by his colleagues and by others interested in the book."  Mathematical Reviews Table of Contents  Introduction
 Some historical examples
 General theorems
 Special methods of summation
 Arithmetic means (1)
 Arithmetic means (2)
 Tauberian theorems for power series
 The methods of Euler and Borel (1)
 The methods of Euler and Borel (2)
 Multiplication of series
 Hausdorff means
 Wiener's Tauberian theorems
 The EulerMacLaurin sum formula
 Appendix I. On the evaluation of certain definite integrals by means of divergent series
 Appendix II. The Fourier kernels of certain methods of summation
 Appendix III. On Riemann and Abel summability
 Appendix IV. On Lambert and Ingham summability
 Appendix V. Two theorems of M. L. Cartwright
 List of books
 List of periodicals
 List of authors
 List of definitions
 General index
