Can someone with Macsyma tell me what Macsyma returns for some
specific elliptic integrals?
I'm interested in the elliptic integrals of the first kind:
integrate(1/sqrt((a^2-t^2)*(b^2-t^2)),t)
and
integrate(1/sqrt((t^2+a^2)*(t^2+b^2)),t)
Other variations would be interesting too.
For the second kind:
integrate(t^2/(sqrt(a^2+t^2)*(b^2-t^2)),t);
and
integrate(t^2/sqrt((t^2+a^2)*(t^2+b^2)),t);
I looked at Mma and these integrals all expressed in terms of the
incomplete elliptic F and E integrals. My current version of the code
returns various inverse Jacobi elliptic functions instead of elliptic
F and E integrasl.
Thanks,
Ray