>>>>> "Denis" == Denis Roegel <denis.roegel at loria.fr> writes:
Denis> Dear all,
Denis> I am beginning to use maxima and the first thing I want to
Denis> do is produce a table of elliptic integrals. I have used
Denis> Ted Woollett's macros nint.mac and it works fine, except
Denis> when I call it more than 1000 times in a row. I am getting
Denis> the output below. Ted had a look at my problem and
I didn't try out nint, but since you're evaluating elliptic integrals,
why not use maxima's elliptic functions? They're likely to be much
faster and more accurate than numerical integration.
Denis> nint(sqrt((1-sqrt(1-b^2)^2*t^2)/(1-t^2)),t,0,0.01),?????????
Your integrand is sqrt((1-sqrt(1-b^2)^2*t^2)/(1-t^2) is equivalent to
sqrt((1-(1-b^2)*t^2)/1-t^2). Let m=1-b^2. Then we have
sqrt((1-m*t^2)/(1-t^2). This is the basic definition of the
incomplete elliptic integral of the second kind:
http://functions.wolfram.com/08.04.07.0002.01:
elliptic_e(z,m) = integrate(sqrt((1-m*t^2)/(1-t^2)), t, 0, sin(z))
Thus, you want to evaluate elliptic_e(asin(0.01), 1-b^2). Maxima can
easily evaluate this.
It would be nice if maxima could determine that
integrate(sqrt((1-m*t^2)/(1-t^2),t) is an elliptic function, but
maxima doesn't know that.
Ray