Ruud H.G. van Tol on Thu, 23 Dec 2021 23:00:30 +0100


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Re: Maple gfun 


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