Definition:Convergent of Continued Fraction/Even

Definition
Let $F$ be a field.

Let $n \in \N \cup \{\infty\}$ be an extended natural number.

Let $C = \left[{a_0, a_1, a_2, \ldots}\right]$ be a continued fraction in $F$ of length $n$.

The even convergents of $\left[{a_0, a_1, a_2, \ldots}\right]$ are the convergents $C_0, C_2, C_4, \ldots$, that is, those with an even subscript.

Also see

 * Definition:Odd Convergent