Unless there is some other code not called by integrate, only the 3rd of
these examples is integrated. The others return the noun form.
After ascertaining that neither a nor b is zero, the answer to item 3 comes
out as the sum of 3 asinh..
B^2*ASINH(2*ABS(B)*T/(ABS(A)*ABS(2*T+2*ABS(B)))
-2*A^2/(ABS(A)*ABS(2*T+2*ABS(B))))
/(2*SQRT(B^2+A^2)*ABS(B))
+B^2*ASINH(2*ABS(B)*T/(ABS(A)*ABS(2*T-2*ABS(B)))
+2*A^2/(ABS(A)*ABS(2*T-2*ABS(B))))
/(2*SQRT(B^2+A^2)*ABS(B))-ASINH(T/ABS(A))$
There are numerical programs for evaluating elliptic integrals, e.g.
elliptic_kc(%)
RJf
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Raymond
> Toy (RT/EUS)
> Sent: Friday, October 19, 2007 1:36 PM
> To: Maxima List
> Subject: Macsyma elliptic integrals
>
>
> 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
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