Subject: Maxima can't solve this integral equation
From: Barton Willis
Date: Fri, 27 Jun 2008 15:48:42 -0500
-----maxima-bounces at math.utexas.edu wrote: -----
>FWIW, I think integrate(sqrt(1-z^4),z,-1,1) is 4/3*elliptic_kc(-1).
The definite integral can also be expressed in terms of gamma functions.
Unfortunately, you need to give Maxima a hint:
(%i15) integrate(sqrt(1-x^4),x,-1,1);
(%o15) integrate(sqrt(1-x^4),x,-1,1)
(%i16) 2 * integrate(sqrt(1-x^4),x,0,1);
(%o16) beta(1/4,3/2)/2
(%i17) float([float(%), 4/3*elliptic_kc(-1)]);
(%o17) [1.74803836952808,1.74803836952808]
Barton