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 _______________________________________________ Help-gsl mailing list [email protected] http://lists.gnu.org/mailman/listinfo/help-gsl
