and set "z" = "r"·"e" "iθ". That theorem has its main interest in the case that the power series has radius of convergence exactly 1: if the radius of convergence is greater than one, the convergence of the power series is uniform for "r" in [0,1] so that the sum is automatically continuous and it follows directly that the limit as "r" tends up to 1 is simply the sum of the "a""n". When the radius is 1 the power series will have some singularity on |"z"| = 1; the assertion is that, nonetheless, if the sum of the "a""n" exists, it is equal to the limit over "r". This therefore fits exactly into the abstract picture.