Some sets of relative stability against perturbations of branching continued fractions with complex elements and variable number of branches (Q2808403)
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scientific article; zbMATH DE number 6584000
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some sets of relative stability against perturbations of branching continued fractions with complex elements and variable number of branches |
scientific article; zbMATH DE number 6584000 |
Statements
23 May 2016
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sets of relative stability against perturbations
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convergence conditions for series of particular form
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Some sets of relative stability against perturbations of branching continued fractions with complex elements and variable number of branches (English)
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The author studies conditions under which infinite branching continued fractions are stable against perturbations of their elements. Formulas of relative errors are derived for the convergents of branching continued fractions with complex partial denominators and numerators that are equal to one. A technique of sets of elements and sets of tail values of the convergents corresponding to them is used to construct sets of relative stability against perturbations. The latter are angular sets and the sets being the exterior of circles on the even fraction floors and the half-planes on its odd floors. Estimates of relative errors are obtained for the convergents of such branching continued fractions.
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