08/08/2014, 12:55 AM

(08/06/2014, 04:38 PM)Gottfried Wrote: I'll also be much interested if I can learn about the approach how to determine the function f(x) which prognoses/approximates the elements of the sequence. I could implement the function f(x) in Pari/Gp but just did not get the clue how one would arrive at it.

Gottfried

Deriving the continuous function is actually pretty straightforward. I'll use exp(x) as an example:

From this, you can derive exp(x).

In general:

By induction:

Now let's try with the problem at hand:

From this, we start recursively solving:

In general:

By induction:

Then, as I posted previously:

~ Jay Daniel Fox