[seqfan] Re: updated list of formulas (conjectures)

[Olivier Gerard]

Simon,

My implicit question was not about what a lgdegf is, even
if your explanation has perhaps been helpful for some
members of seqfan.

I understand that f(x) is good device for expressing rational functions.

But I was wondering why you used this explicit f(x) notation in this very
linear case where you did not use it for many ogfs and egfs.
It complicates a little the parsing for me.

Also, your conjectures are of the following kinds:

  88668 ogf
   3639 ogf_with_Euler_Transform
   2780 egf
    791 lgdegf
    510 lgdogf
     28 egf_with_Euler_Transform

But we have tens of gf transforms available thanks to the work of Neil
Sloane, Berstein, Bower, yours truly.  Some sequences have been explicitely
constructed with them. I am surprised none
of them shows up as positive in your analysis.

Olivier



On Mon, Feb 14, 2011 at 14:57, Simon Plouffe <simon.plouffe at gmail.com>wrote:

>
>
> Hello,
>
>  lgdegf means that the exponential of the integral
> of x+2 is the exponential generating function,
>
>  since we have that x + 2 - f(x) = 0 then
>
>  f(x) = x + 2
>
>  by doing exactly the inverse
>
>  exp(int(x+2,x));
>
>  we get the known generating function of that
> sequence which is : exp(2*x + x^2/2) :
>
>