2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135737Jacobi's elliptic integrals and elliptic functions arise naturally from the Schwarz-Christoffel conformal transformation of the upper half plane onto a rectangle. In this paper we study generalized elliptic integrals which arise from the analogous mapping of the upper half plane onto a quadrilateral and obtain sharp monotonicity and convexity properties for certain combinations of these integrals, thus generalizing analogous well-known results for classical conformal capacity and quasiconformal distortion functions.32 pages, 4 figuresClassical Analysis and ODEsComplex Variables33B15, 30C62text