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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

1. Lane, R. E. and Wall, H. S., Continued fractions with absolutely convergent even and- odd parts, Trans. Amer. Math. Soc, 67 (1949), 368-80.Google Scholar
2. Scott, W. T. and Wall, H. S., A convergence theorem for continued fractions, Trans. Amer. Math. Soc, 47 (1940), 155-72.Google Scholar
3. Van Vleck, E. B., On the convergence of continued fractions with complex elements, Trans. Amer. Math. Soc, 2 (1901), 215–33.Google Scholar
4. Wall, H. S., Analytic theory of continued fractions (New York, 1948).Google Scholar
5. Wall, H. S., Continued fractions and cross-ratio groups of Cremona transformations, Bull. Amer. Math. Soc, 40 (1934), 578–92.Google Scholar