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, ... .

Read more about this topic:  Continued Fraction

Famous quotes containing the word continued:

    The cause of Sense, is the External Body, or Object, which presseth the organ proper to each Sense, either immediately, as in the Taste and Touch; or mediately, as in Seeing, Hearing, and Smelling: which pressure, by the mediation of Nerves, and other strings, and membranes of the body, continued inwards to the Brain, and Heart, causeth there a resistance, or counter- pressure, or endeavor of the heart, to deliver it self: which endeavor because Outward, seemeth to be some matter without.
    Thomas Hobbes (1579–1688)