Definition:Continued Fraction/Simple/Infinite
< Definition:Continued Fraction | Simple(Redirected from Definition:Simple Infinite Continued Fraction)
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Definition
Let $\R$ be the field of real numbers.
A simple infinite continued fraction is a infinite continued fraction in $\R$ whose partial quotients are integers that are strictly positive, except perhaps the first.
That is, it is a sequence $a: \N_{\ge 0} \to \Z$ with $a_n > 0$ for $n > 0$.
Also known as
A simple infinite continued fraction can be abbreviated SICF.
It is also known as a regular infinite continued fraction.
The order of the words can be varied, that is infinite simple continued fraction for example, but $\mathsf{Pr} \infty \mathsf{fWiki}$ strives for consistency and does not use that form.
Also see
- Definition:Value of Infinite Continued Fraction
- Definition:Simple Finite Continued Fraction
- Correspondence between Irrational Numbers and Simple Infinite Continued Fractions
Sources
- Weisstein, Eric W. "Simple Continued Fraction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SimpleContinuedFraction.html