Author | Brezinski, Claude. author |
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Title | History of Continued Fractions and Padรฉ Approximants [electronic resource] / by Claude Brezinski |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991 |
Connect to | http://dx.doi.org/10.1007/978-3-642-58169-4 |
Descript | VIII, 551 p. online resource |
1 The Early Ages -- 1.1 Euclidโs algorithm -- 1.2 The square root -- 1.3 Indeterminate equations -- 1.4 History of notations -- 2 The First Steps -- 2.1 Ascending continued fractions -- 2.2 The birth of continued fractions -- 2.3 Miscellaneous contributions -- 2.4 Pellโs equation -- 3 The Beginning of the Theory -- 3.1 Brouncker and Wallis -- 3.2 Huygens -- 3.3 Number theory -- 4 Golden Age -- 4.1 Euler -- 4.2 Lambert -- 4.3 Lagrange -- 4.4 Miscellaneous contributions -- 4.5 The birth of Padรฉ approximants -- 5 Maturity -- 5.1 Arithmetical continued fractions -- 5.2 Algebraic continued fractions -- 5.3 Varia -- 6 The Modern Times -- 6.1 Number theory -- 6.2 Set and probability theories -- 6.3 Convergence and analytic theory -- 6.4 Padรฉ approximants -- 6.5 Extensions and applications -- Documents -- Document 1: Lโalgรจbre des gรฉomรจtres grecs -- Document 2: Histoire de lโAcadรฉmie Royale des Sciences -- Document 3: Encyclopรฉdie (Supplรฉment) -- Document 4: Elementary Mathematics from an advanced standpoint -- Document 5: Sur quelques applications des fractions continues -- Document 6: Rapport sur un Mรฉmoire de M. Stieltjes -- Document 7: Correspondance dโHermite et de Stieltjes -- Document 8: Notice sur les travaux et titres -- Document 9: Note annexe sur les fractions continues -- Scientific Bibliography -- Works -- Historical Bibliography -- Name Index