In article <324FEC1A.email@example.com> David Ullrich <firstname.lastname@example.org> writes: > Christopher wrote: > > Please tell me how to prove simply that an analytic function is a function of > > z only, no z_bar. > > Using z* for the conjugate of z: > > You need to state the conclusion more precisely before this can be > proved. We all agree that f(z) = z^2 is analytic, but f(z) = g(z*) for a > certain function g , so f _is_ "a function of z*".
Indeed. I always prefer to relate the term "analytic" to a variable, i.e. "the function f(z) is analytic in z" (this is implied by many mathematicians but I prefer to make it explicit). Now I think the question is: can a function g(z, z*) be analytical in z? Still the answer can be affirmative; consider: g(u, v) = u + v* in that case g(z, z*) = 2z and is analytic in z (but not in z*). -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/