High Quality Content by WIKIPEDIA articles! In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients. It is named after Norwegian mathematician Niels Henrik Abel. Theorem Let a = {ak: k >= 0} be any sequence of real or complex numbers and let be the power series with coefficients a. Suppose that the series converges. Then where the variable z is supposed to be real, or, more generally, to lie within any Stoltz angle, that is, a region of the open unit disk where for some M. Without this restriction, the equality may fail to hold.

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