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Continued Fraction Fundamental Recurrence Relation


For a simple continued fraction x=[a_0,a_1,...] with convergents p_n/q_n, the fundamental recurrence relation is given by

 p_nq_(n-1)-p_(n-1)q_n=(-1)^(n+1).

See also

Simple Continued Fraction, Continued Fraction

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References

Olds, C. D. Continued Fractions. New York: Random House, p. 27, 1963.

Referenced on Wolfram|Alpha

Continued Fraction Fundamental Recurrence Relation

Cite this as:

Weisstein, Eric W. "Continued Fraction Fundamental Recurrence Relation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ContinuedFractionFundamentalRecurrenceRelation.html

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