  Jacobi'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.
