Computer aided solution of the invariance equation for two-variable Stolarsky means

We solve the so-called invariance equation in the class of two-variable Sto-be valid. We recall that, for pq(p − q) = 0 and x = y, the Stolarsky mean S p,q is defined by S p,q (x, y) := q(x p − y p) p(x q − y q) 1 p−q. In the proof first we approximate the Stolarsky mean and we use the computer algebra system Maple V Release 9 to compute the Taylor expansion of the approximation up to 12th order, which enables us to describe all the cases of the equality.