Abstract
Let {an}∞1 and {θn}∞0 be the sequences of partial quotients and approximation coefficients for the continued fraction expansion of an irrational number. We will provide a function f such that an+1 = f(θn±1, θn). In tandem with a formula due to Dajani and Kraaikamp, we will write θn±1 as a function of (θn∓1, θn), revealing an elegant symmetry in this classical sequence and allowing for its recovery from a pair of consecutive terms.
Original language | English |
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Pages (from-to) | 3681-3688 |
Number of pages | 8 |
Journal | Proceedings of the American Mathematical Society |
Volume | 141 |
Issue number | 11 |
DOIs | |
State | Published - 27 Aug 2013 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics