Is there a way to transform the continued fraction ?

[lvl107]

  Hello, Everyone.

    Is there a way to transform LHS to RHS ?

    Thanks in advance for your time and help.

         Regards.

Message was edited by: Loi Le

[AlvaroDíaz]

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.

[lvl107]

   I'm sorry, my question should be :

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

      Best Regards.

[AlvaroDíaz]

Here a way.

Regards.

[lvl107]

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

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

     Regards.

[AlvaroDíaz]

Yep. Here it is. I know that in prime there are a function for hidding symbolics values, but don't remember which.

Best regards.

[AlvaroDíaz · Accepted solution]

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.