Brezinski, Claude History of continued fractions and Padé approximants. (English, French) Zbl 0714.01001 Springer Series in Computational Mathematics, 12. Berlin etc.: Springer- Verlag. 551 p. DM 188.00 (1991). With a style reminiscent of L. E. Dickson’s in “History of the theory of numbers”, the author treats us to a thorough excursion through the many topics related to continued fractions. Six chapters take us chronologically from Greek times to the present through a rich variety of investigations in number theory, analysis and approximations, as the concepts slowly crystallized and became formalized. The narration (in English) is punctuated by many excerpts from works quoted in English, French and Latin. The value of the book is considerably enhanced by its appendices: 9 “documents” or passages quoted at length from mainly French expository sources, a scientific bibliography of 2302 items, a list of 78 collected works, a historical bibliography of 478 items and an index of names with basic biographical information. Purchase of this book is recommended for both reference and frequent browsing. Reviewer: E.J.Barbeau Cited in 2 ReviewsCited in 65 Documents MSC: 01A05 General histories, source books 11-03 History of number theory 30-03 History of functions of a complex variable 40-03 History of sequences, series, summability 41-03 History of approximations and expansions 11A55 Continued fractions 41A21 Padé approximation 11J70 Continued fractions and generalizations 30B70 Continued fractions; complex-analytic aspects 40A15 Convergence and divergence of continued fractions Keywords:continued fractions; Padé approximations; approximation by rationals and rational functions; number theory; analysis; bibliography PDFBibTeX XMLCite \textit{C. Brezinski}, History of continued fractions and Padé approximants. Berlin etc.: Springer-Verlag (1991; Zbl 0714.01001)