Œuvres Complètes I - Collected Papers I

This is a new annotated edition of Thomas J. Stieltjes' Collected Papers published earlier in 1914 (Vol. I) and 1918 (Vol. II) by Noordhoff, Groningen, in French. The new edition is published by Springer-Verlag in two volumes (only available in one set) on the occasion of the 100th anniversary of Stieltjes' death (1894). This book is of great interest for all mathematicians anxious to understand the impact of Stieltjes' work on modern mathematics, and in particular on the theory of orthogonal polynomials and continued fractions. The book contains, besides the reproduction of Stieltjes' papers, about 75 pages of commentaries by contemporary mathematicians on Stieltjes' work as well as an English translation of his main paper "Recherches sur les fractions continues" and of his short note regarding the Riemann hypothesis.

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The year 1994, one century after Thomas Stieltjes' death, is a fitting time to look back and assess the impact of Stieltjes' work on the development of mathematics. The idea to combine such an assessment with a new edition of the Collected Papers of T. J. Stieltjes, was born in 1990 during a discussion with Richard Askey in Amsterdam. The present edition, which consists of two volumes, is mainly a reissue of the CEuvres Completes of Thomas Jan Stieltjes, published by Noordhoff, Groningen in the period 1914-18. I have added a short biography and four commentaries on parts of Stieltjes' work, written by specialists. Translations of his papers "Sur une fonction uniforme" and "Recherches sur les fractions continues" are also included. The first paper contains the "proof" of the Rie mann hypothesis, and the second paper, which is generally considered to be his most important one, contains the introduction of the Stieltjes integral. A Bibliography of Stieltjes is included in both volumes for the convenience of the reader. I want to thank those who have helped and stimulated me during the preparation of these volumes: the Wiskundig Genootschap for generously ac cepting my plans and sponsoring the preparation of the present edition, and colleagues from Toulouse, the city Stieltjes owes so much to. A special word of thanks is due to Walter Van Assche (Katholieke Universiteit Leuven) who has critically read the final versions of almost all contributions and translations.