指数积分截面零点的极限曲线
Limit curves for zeros of sections of exponential integrals
摘要：
研究了由指数积分定义的整函数族的幂级数部分和零点的渐近性态。时间复杂度为O（n），时间复杂度为O（n）。我们发现，零点接近曲线的速度取决于指数积分中被积函数的奇点/零点的阶数。作为我们的研究结果的应用，我们得到的结果有关的幂级数的部分和的零点的第一类贝塞尔函数。
英文摘要：
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.
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