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:
“That, upon the whole, we may conclude that the Christian religion not only was at first attended with miracles, but even at this day cannot be believed by any reasonable person without one. Mere reason is insufficient to convince us of its veracity: And whoever is moved by Faith to assent to it, is conscious of a continued miracle in his own person, which subverts all the principles of his understanding, and gives him a determination to believe what is most contrary to custom and experience.”
—David Hume (1711–1776)