Definition:Partial Quotient

Definition
Let $k$ be a field. Let $\sequence {a_n}_{n \ge 0}$ 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