Definition:Partial Quotient

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 quotient is the $n$th term $a_n$.

Also known as

A partial quotient is also known as a partial denominator, particularly in the case of a general continued fraction.

Also see

• Definition:Complete Quotient
• Definition:Sequence of Partial Quotients
• Definition:Sequence of Complete Quotients

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