  Multiple elliptic integrals related to the generalized Clebsch-Gordan (CG)
integral are of importance in many areas in physics and special functions
theory. Zhou has introduced and applied Legendre function-based techniques to
prove symbolic evaluations for integrals of CG form involving twofold and
threefold products of complete elliptic integral expressions, and this includes
Zhou's remarkable proof of an open problem due to Wan. The foregoing
considerations motivate the results introduced in this article, in which we
prove closed-form evaluations for new CG-type integrals that involve threefold
products of the complete elliptic integrals $K$ and $E$. Our methods are based
on the use of fractional derivative operators, via a variant of a technique we
had previously referred to as semi-integration by parts.
