I think there is a bug in `evalf/EllipticF` function over the complex numbers (at least in MapleVR5). Consider the following input:
(The result is rather long expression with elliptic integral of the ﬁrst kind functions; the second term was added to produce O(1) result for large (a-b)). Now consider, for example
The error is obvious — the integral of real valued function along the real axis should be real. Moreover, when the ‘int‘ is invoked with real limits or symbols `assume`d to be real it gives manifestly real answer (probably correct).
Well, it gets more and more curious:
a nice (but unfortunately wrong) result. Changing the assume-line to
seems to produce the correct result, as does also the explicit command