  A magic series is a set of natural numbers that, by virtue of its size, sum,
and maximum value, could fill a row of a normal magic square. In this paper, we
derive an exact two-dimensional integral representation for the number of magic
series of order N. By applying the stationary phase approximation, we develop
an expansion in powers of 1/N for the number of magic series and calculate the
first few terms. We find excellent agreement between our approximation and the
known exact values. Related results are presented for magic cube and hypercube
series, bimagic series, and trimagic series.
