2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136222A two-parameter generalization of the complete elliptic integral of second kind is expressed in terms of the Appell function $F_{4}$. This function is further reduced to a quite simple bilinear form in the complete elliptic integrals $K$ and $E$. The physical applications are briefly mentioned.Mathematical Physicstext