Talk:Continued fraction

Task name

Should the task name be Generalized continued fractions? Both Mathworld and Wikipedia note that these is more properly called generalized continued fractions and that the term continued fraction is most often used for simple continued fractions. —Sonia 21:41, 27 February 2012 (UTC)

In principal Continued Fractions are generalized in the sense that they work for all numbers. In computer terms it is often required to handle Integers, Rationals, Reals, and Complex Numbers seperately. For this task it is sufficent for cf to work with Integers. A solution which switches between Integer and Floating Point will not be able to generate the exact solution that for instance the Python and Haskell solutions do. Having to implement cf for all types of number would make the task more time consuming and detract from the structure of the solution: a CF object; generators for aN and bN; and translation from the exact CF object to a real number.--Nigel Galloway 16:11, 29 February 2012 (UTC)

Subscript convention

Both Mathworld and Wikipedia use a subscript convention different that what is used in the task description. It might be best to match their convention. —Sonia 21:43, 27 February 2012 (UTC)

Related tasks

One might be Thiele's interpolation formula. —Sonia 21:59, 27 February 2012 (UTC)

When the structure of the solution: a CF object; generators for aN and bN; and translation from the exact CF object to a real number, is established then we can tackle the Thiele task properly. Note that the cf representation for: arcsin is http://www4b.wolframalpha.com/input/?i=continued%20fraction%20arcsin%28x%29&lk=2; arccos is http://www.wolframalpha.com/input/?i=arcos%28z%29+continued+fraction+representations; and arctan is http://www4b.wolframalpha.com/input/?i=continued%20fraction%20arctan%28x%29&lk=2.