We can extend our notation to the case of two parameters n and m that can go to infinity independently at different rates. For a given function g. n; m/, we denote by O. g.n; m// the set of functions O. g.n; m// D ff .n; m/ W there exist positive constants c, n0, and m0 such that 0 f .n; m/ cg. n; m/ for all n n0 or m m0g : Give corresponding definitions for .g. n; m// and ‚.g. n; m//.