Definition:Complete Quotient

Definition
Let $x$ be an irrational number.

The sequence of complete quotients is defined recursively by:
 * $\alpha_0 = x$
 * $\alpha_{n + 1} = \dfrac 1 {\fractpart {\alpha_n} }$

where $\fractpart {\, \cdot \,}$ denotes fractional part.

Also see

 * Definition:Sequence of Complete Quotients
 * Definition:Sequence of Partial Quotients
 * Definition:Convergent of Continued Fraction