Chain Sequence (continued Fraction)
In the analytic theory of continued fractions, a chain sequence is an infinite sequence {an} of non-negative real numbers chained together with another sequence {gn} of non-negative real numbers by the equations
where either (a) 0 ≤ gn < 1, or (b) 0 < gn ≤ 1. Chain sequences arise in the study of the convergence problem – both in connection with the parabola theorem, and also as part of the theory of positive definite continued fractions.
The infinite continued fraction of Worpitzky's theorem contains a chain sequence. A closely related theorem shows that
converges uniformly on the closed unit disk |z| ≤ 1 if the coefficients {an} are a chain sequence.
Read more about Chain Sequence (continued Fraction): An Example
Famous quotes containing the words chain and/or sequence:
“The name of the town isn’t important. It’s the one that’s just twenty-eight minutes from the big city. Twenty-three if you catch the morning express. It’s on a river and it’s got houses and stores and churches. And a main street. Nothing fancy like Broadway or Market, just plain Broadway. Drug, dry good, shoes. Those horrible little chain stores that breed like rabbits.”
—Joseph L. Mankiewicz (1909–1993)
“Reminiscences, even extensive ones, do not always amount to an autobiography.... For autobiography has to do with time, with sequence and what makes up the continuous flow of life. Here, I am talking of a space, of moments and discontinuities. For even if months and years appear here, it is in the form they have in the moment of recollection. This strange form—it may be called fleeting or eternal—is in neither case the stuff that life is made of.”
—Walter Benjamin (1892–1940)