Re: Maple gfun

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

On 2021-12-23 20:22, Bill Allombert wrote:
> [...]
> A new function (available in the git branch bill-serdiffdep).
>
> ? S=sum(i=0,20,binomial(3*i,i)*T^i)+O(T^21);
> ? serdiffdep(S,3,3)
> %3 = [(27*T^2-4*T)*x^2+(54*T-2)*x+6,0]
>
> So S satisfies the linear equation
>
> (27*T^2-4*T)*S'' + (54*T-2)*S' +6*S = 0
>
> ? S=exp(T^2)+T^2
> %4 =
> %1+2*T^2+1/2*T^4+1/6*T^6+1/24*T^8+1/120*T^10+1/720*T^12+1/5040*T^14+1/40320*T^16+O(T^18)
> ? serdiffdep(S,3,3)
> %5 = [x-2*T,-2*T^3+2*T]
>
> So S satisfies the linear equation:
> S'-2*T*S = -2*T^3+2*T
>
> Is it what you are looking for ?

Nice!

I coined up gfun, because I was impressed by everything it can do.

I downloaded the package, and it has a textual maple code file,
with quite some data in it. I didn't parse it yet,
to see what the contents are.

Maple has a built in way to generate code:
https://www.maplesoft.com/support/help/Maple/view.aspx?path=CodeGeneration&cid=533

If I find the time, I'll let it transform
the gfun-module into something legible,
to find out more.

-- Ruud