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On the convergence of continued radicals with applications to polynomial equations

โœ Scribed by R.I. Andrushkiw

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
323 KB
Volume
319
Category
Article
ISSN
0016-0032

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โœฆ Synopsis

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 the case when r, is an integer > 2. Some examples illustrating the applicability of continued radicals to polynomial equations, and their relation to continued fractions, are given.

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