1. The problem statement, all variables and given/known data I can't figure out what my professor means in the last two lines: I'm trying to prove why the product of two analytic functions is analytic, and I think that I am going to need to use a similar construction. 3. The attempt at a solution So far to prove the product is analytic, I have said that for f(x) convergent for x<R1 g(x) convergent for x<R2 Then, (f*g)(x) is convergent for x<min(R1,R2), then, I think I can say that for some rearrnagment of terms, (f*g)(x) = sum n=0 to infinity of (c_n x^n), but I'm not sure if or why I could make that last step. Thanks!