Definition:Partial Denominator
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Definition
Let $k$ be a field.
Let $\sequence {a_n}_{n \mathop \ge 0}$ be a continued fraction in $k$, either finite or infinite.
Let $n \ge 0$ be a natural number.
The $n$th partial denominator is the $n$th term $a_n$.
Also known as
A partial denominator is also known as a partial quotient, particularly in the case of a simple continued fraction.
However, this is also used for the quotient in the context of integer division, or in the more general context of a Euclidean domain.
Also see
- Results about partial denominators can be found here.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continued fraction
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): partial quotient: 2.
- Weisstein, Eric W. "Partial Denominator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PartialDenominator.html