[Help-gsl] Incomplete elliptic integral E(phi, k) decreasing with phi?

[Liam Healy]

For the incomplete elliptic integral of the second kind E(phi,k)
the definition given in
http://mathworld.wolfram.com/EllipticIntegraloftheSecondKind.html
and Abramowitz & Stegun (I think, my copy is not with me now)
has an integrand sqrt(1 - k^2 sin^2 theta), which is always non-negative.
Therefore, this function should be monotonically non-decreasing as phi
increases.
Yet I try gsl_sf_ellint_E_e
for phi = 0.5pi and k=0.5, I find the value returned is 1.46746 (which
agrees with the result from the complete elliptic integral as it
should),
and for phi= 0.6pi and k=0.5, value is 1.19394.  In fact, for phi=pi,
I get essentially 0, when it looks like I should get 2*1.46746 because
sin^2 is symmetric about pi/2.  If this function is domain limited,
should it signal an EDOM error if given phi>pi/2?

Liam