  We are interested in studying the asymptotic behavior of the zeros of partial
sums of power series for a family of entire functions defined by exponential
integrals. The zeros grow on the order of O(n), and after rescaling we
explicitly calculate their limit curve. We find that the rate that the zeros
approach the curve depends on the order of the singularities/zeros of the
integrand in the exponential integrals. As an application of our findings we
derive results concerning the zeros of partial sums of power series for Bessel
functions of the first kind.
