1. A theorem stating that if a power series in z converges for z = a, it converges absolutely for z < a .

2. A theorem stating that if a power series in z converges to f (z ) for z < 1 and to a for z = 1, then the limit of f (z ) as z approaches 1 equals a.

3. A theorem stating that if the three series with nth term a_n , b_n , and c_n = a₀b_n + a₁b_n-1 + ... + a_nb₀, respectively, converge, then the third series equals the product of the first two series.