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lvl10720-Turquoise
20-Turquoise
October 11, 2015
Solved

Is there a way to transform the continued fraction ?

  Hello, Everyone.

Transform.PNG

    Is there a way to transform LHS to RHS ?

    Thanks in advance for your time and help.

         Regards.

Message was edited by: Loi Le

AlvaroDíazAnswer
12-Amethyst
October 15, 2015

Oh, I forgot to tell that you must to provide the transformation sequence ci for get the generalized from the canonical expansion. If not, there are a lot of chances to get any sequence. The canonical is unique, the generalized not.

Hope this helps.

cf.gif

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6 replies

AlvaroDíaz12-Amethyst
12-Amethyst
October 13, 2015

Sure. By a theorem. First, notice that RHS isn't a continued fraction, is a generalized one. What you show is a special case of the equivalence transformation, making ci=1. See Generalized continued fraction - Wikipedia, the free encyclopedia

Regards.

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lvl10720-TurquoiseAuthor
20-Turquoise
October 14, 2015

   I'm sorry, my question should be :

a change.PNG

  How to make a change from the continued fraction to the generalized continued fraction ?

      Best Regards.

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AlvaroDíaz12-Amethyst
12-Amethyst
October 14, 2015

Here a way.

Regards.

ContFrac.gif

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lvl10720-TurquoiseAuthor
20-Turquoise
October 15, 2015

  I greatly appreciate your time and help, Alvaro.   And I have a similar question is :

(3).PNG

  Is it possible to create a program function with the input and output like as the above or a similar ?

     Regards.

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