# elliptic integrals - again

Discussion in 'Maple' started by Michael Zedler, Jul 13, 2005.

1. ### Michael ZedlerGuest

Hello,

isn't solved yet, and apparently I can't convince Maple to help me.

X:=sqrt(((z-1)^2+a^2)*((z+1)^2+a^2));
a^2/(-z^2+1+(((z-1)^2+a^2)*((z+1)^2+a^2))^(1/2));
int(%,z=0..infinity);

How can these things be solved?

Kind regards,
Michael

Michael Zedler, Jul 13, 2005

2. ### Michael ZedlerGuest

sorry, I I posted the wrong stuff. It should read

X:=sqrt(((z-1)^2+a^2)*((z+1)^2+a^2));
int(ln(-z^2+1+X)-ln(a^2),z=0..infinity);

Michael

Michael Zedler, Jul 13, 2005

3. ### G. A. EdgarGuest

X:=sqrt(((z-1)^2+a^2)*((z+1)^2+a^2));
Y:=a^2/(-z^2+1+(((z-1)^2+a^2)*((z+1)^2+a^2))^(1/2));

int(X,z) and int(Y,z) are elliptic integrals, Maple evaluates
them in terms of arctan, EllipticE, EllipticF, EllipticPi.
Sometimes with complex arguments.

The problem of int(Y,z=0..infinity), then, is the problem of the
limiting behavior of those functions.

G. A. Edgar, Jul 13, 2005
4. ### snooflyGuest

the answer appears to be 106

snoofly, Jul 14, 2005
5. ### snooflyGuest

sorry, scrub that - wrong calculation

snoofly, Jul 14, 2005