Divergent series. 2nd (textually unaltered) ed. (English) Zbl 0897.01044

Hardy, G. H.

New York, NY: Chelsea. xvi, 396 p. (1991).

[The first ed. of this monograph has been reviewed (1949; Zbl 0032.05801).]
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 Euler-MacLaurin 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.

MSC:

01A75	Collected or selected works; reprintings or translations of classics
40-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to sequences, series, summability
40-03	History of sequences, series, summability

Keywords:

Euler; Borel; Hausdorff means; Tauberian theorems; Euler-MacLaurin sum formula; Fourier kernels; Abel summability; Ingham summability; theorems of M. L. Cartwright