Definition:Continued Fraction/Notation
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Notation for Continued Fraction
A continued fraction can be denoted using ellipsis:
- $a_0 + \cfrac 1 {a_1 + \cfrac 1 {a_2 + \cfrac 1 {\ddots \cfrac {} {} } } }$
Another notation that can sometimes be seen is:
- $a_0 + \dfrac 1 {a_1 +} \dfrac 1 {a_2 +} \dfrac 1 {a_3 + \cdots}$
By definition, a continued fraction is its sequence of partial denominators and can thus be denoted:
- $\sequence {a_n}_{n \mathop \ge 0}$
- $\sqbrk {a_0; a_1, a_2, \ldots}$
- $\sqbrk {a_0, a_1, a_2, \ldots}$
where the last two notations are usually reserved for its value.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continued fraction
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): continued fraction