History of Continued Fractions and Padé Approximants

1. Front Matter

   Pages i-viii

   PDF

2. Introduction

   • Claude Brezinski

   Pages 1-2

3. The Early Ages

   • Claude Brezinski

   Pages 3-50

4. The First Steps

   • Claude Brezinski

   Pages 51-75

5. The Beginning of the Theory

   • Claude Brezinski

   Pages 77-96

6. Golden Age

   • Claude Brezinski

   Pages 97-140

7. Maturity

   • Claude Brezinski

   Pages 141-259

8. The Modern Times

   • Claude Brezinski

   Pages 261-311

9. Back Matter

   Pages 347-462

   PDF

The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great­ est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak­ ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im­ portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran­ scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con­ tinued fractions are also used in number theory, computer science, automata, electronics, etc ...

• Geschichte der Mathematik
• History of Mathematics
• Pade Approximation
• Zahlentheorie
• differential equation
• number theory
• orthogonal polynomials

• Laboratoire d’Analyse Numérique et d’Optimisation UFR IEEA-M3, Université des Sciences et Techniques, Villeneuve d’Ascq Cedex, France

  Claude Brezinski

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