Hello,
i have discovered 2 programs included in maxima, but whose function is not
very clear to me.
One is levin, it has been mentioned recently here. Acccording to the
comments it is used to improve convergence of "numerical" sums, such as:
levin_u_sum(1/n^2,n,1,10);
However i have tried to add a parameter, such as:
g: rat(levin_u_sum(t^n/n^2,n,1,10));
which results in something looking like a Pad? approximant in the variable
t. I have checked for various values of t like 1/3, 1/5 that this formula
reproduces what one gets by directly substituting t=1/3 ... before computing
levin, so the formula seems correct. Is this an intended use of levin,
and does this produce an alternative way to get Pad? approximants - which
would be interesting because the pade command in maxima saturates very fast?
The other is hyperint, for which i have not found any documentation. However
trying it, i have found very supicious result:
niobe% maxima
(%i1) load(hyperint);
...
(%i3) hyper_int(1/sqrt(x*(x+1)*(x-1)),x);
;
; Warning: This function is undefined:
; GAMMA
1 1 5 2 2
2 hypergeometric([-, -], [-], x ) x sqrt(1 - x )
4 2 4
(%o3) ------------------------------------------------
3
sqrt(x - x)
First the gamma function is well defined in maxima, and second the
integral in question is obviously elliptic, and i have not found formula
which reduces incomplete elliptic integral to hypergeometric functions
(in contrast with complete integral). Maybe there exists one, but i am not
aware.
--
Michel Talon