Definition:Convergent of Continued Fraction/Even
< Definition:Convergent of Continued Fraction(Redirected from Definition:Even Convergent)
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Definition
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 even convergents of $\sqbrk {a_0, a_1, a_2, \ldots}$ are the convergents $C_0, C_2, C_4, \ldots$, that is, those with an even subscript.