×

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

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
PDFBibTeX XMLCite