Definition:Convergent of Continued Fraction/Odd

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Let $F$ be a field.

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

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

The odd convergents of $\sqbrk {a_0, a_1, a_2, \ldots}$ are the convergents $C_1, C_3, C_5, \ldots$, that is, those with an odd subscript.

Also see