[seqfan] Re: updated list of formulas (conjectures)
Olivier Gerard
olivier.gerard at gmail.com
Mon Feb 14 15:32:38 CET 2011
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) :
>
>
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