Definition:Partial Denominator

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

• Definition:Sequence of Partial Denominators

• 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