On exterior moduli of quadrilaterals and special functions
  In this paper two identities involving a function defined by the complete elliptic integrals of the first and second kinds are proved. Some functional inequalities and elementary estimates for this function are also derived from the properties of monotonicity and convexity of this function. As applications, some functional inequalities and the growth of the exterior modulus of a rectangle are studied. 
Matti Vuorinen and Xiaohui Zhang
math.CA