triaxial ellipsoid with circular equator does not match ellipsoid

[pkienzle]

Comparing ellipsoid with triaxial ellipsoid where the equatorial major and minor axes of the triaxial ellipsoid match the equatorial radius of the ellipsoid yields different results. This is true in SasView 3.1.x as well, for both 1D and 2D models.

[pkienzle]

Note: formula for form factor does not match calculation in the triaxial ellipsoid (1D).

Formula inside integral in help says:

    Phi^2[ q R_a^2 cos^2(pi/2 x) + q R_b^2 sin^2(pi/2 y)(1-y^2) + R_c^2 y^2 ]

Code says:

    Phi^2[ q sqrt(R_a^2 cos^2(pi/2 x) + R_b^2 sin^2(pi/2 y)(1-y^2) + R_c^2 y^2) ]

[pkienzle]

The following gives an alternative formula for the 1-D triaxial ellipsoid:

​http://iopscience.iop.org/0022-3727/4/1/310

This gives a result consistent with ellipsoid.