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

New Clebsch-Gordan-type integrals involving threefold products of complete elliptic integrals