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On the solution of polynomial equations using continued fractions

โœ Scribed by Alkiviadis G. Akritas


Book ID
113162074
Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
343 KB
Volume
9
Category
Article
ISSN
0020-0190

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๐Ÿ“œ SIMILAR VOLUMES


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โœ Y.H. Ku ๐Ÿ“‚ Article ๐Ÿ“… 1972 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 381 KB

This note jollows the work of Lagrange and Euler and gives the essential steps for reaching a solution of the Boole and the Riccati equations with the help of continued fractions. The resulta are compared with the series solutions (which may be recognized in closed form for simple caaea) obtained by

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The class of continued radicals r,J(ar +?/(a, +Iq(a, + . . .))) is investigated for the case where a, > O,r, > 2. Results concerning the convergence of continued radicals are obtained and an error estimate is givenfor the approximating sequence t, = 'q(al +';/(a, + ... +';/(a.))), n = 1,2,. . , in