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Analytic expressions for continued fractions over a vector space


Author: F. A. Roach
Journal: Proc. Amer. Math. Soc. 56 (1976), 135-139
MSC: Primary 30A22
DOI: https://doi.org/10.1090/S0002-9939-1976-0404599-7
MathSciNet review: 0404599
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Abstract: In previous papers, we considered continued fractions obtained from a type of ``geometric reciprocal". In this paper we develop certain ``analytical'' formulas for such continued fractions and, by using these formulas, obtain results analogous to certain classical theorems for ordinary continued fractions.


References [Enhancements On Off] (What's this?)

  • [1] F. A. Roach, Continued fractions over an inner product space, Proc. Amer. Math. Soc. 24 (1970), 576-582. MR 0412654 (54:776)
  • [2] -, The parabola theorem for continued fractions over a vector space, Proc. Amer. Math. Soc. 28 (1971), 137-146. MR 43 #762. MR 0275004 (43:762)
  • [3] H. S. Wall, Analytic theory of continued fractions, Van Nostrand, New York, 1948. MR 10, 32. MR 0025596 (10:32d)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0404599-7
Keywords: Continued fractions
Article copyright: © Copyright 1976 American Mathematical Society

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