Generalized elliptic integrals (Q2378571)

Jacobi's elliptic integrals and elliptic functions arise naturally from the Schwarz-Christoffel conformal transformation of the upper half plane onto a rectangle. Here the authors study generalized elliptic integrals which arise from the analogous mapping of the upper half-plane onto 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. They also give an algorithm for the computation of the modulus of the quadrilateral.