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Continued Fractions with Absolutely Convergent Even or Odd Part

Published online by Cambridge University Press:  20 November 2018

David F. Dawson
David F. Dawson*
Affiliation:
University of Missouri
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The purpose of this paper is to give conditions under which the absolute convergence of the subsequence of odd or of even approximants to a continued fraction implies convergence of the continued fraction. In § 2 we consider the problem in general, and in § 3 we impose a condition which gives absolute convergence of the odd or of the even part of the continued fraction and state conditions which imply convergence of the continued fraction.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 131 - 140
Copyright
Copyright © Canadian Mathematical Society 1959

References

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5. Wall, H. S., Continued fractions and cross-ratio groups of Cremona transformations, Bull. Amer. Math. Soc, 40 (1934), 578–92.Google Scholar