Continued Fraction - Notations For Continued Fractions

Notations For Continued Fractions

The integers a₀, a₁ etc., are called the quotients of the continued fraction. One can abbreviate the continued fraction

as

,

or in the notation of Pringsheim as

,

or in another related notation as

Sometimes angle brackets are used, like this:

The semicolon in the square and angle bracket notations is sometimes replaced by a comma.

One may also define infinite simple continued fractions as limits:

This limit exists for any choice of a₀ and positive integers a₁, a₂, ... .