论文标题
交错，赫维兹系列的积分和微分方程
Interlacing, integrals of Hurwitz series and differential equations
论文作者
论文摘要
在本文中，我们首先介绍了Hurwitz系列的Unlacting，该系列可以看作是交错的倒数，并开发了Hurwitz系列的Unlaceing，Unlacting，nuthlaceing和Entevers的基本属性。然后，我们证明，赫维兹系列乘以基础元素的乘法也可以作为交织插条重写，并根据积分和哈玛德产品提供明确的乘法公式。最后，我们调查了自然指数函数$ \ exp $，并使用$ \ exp $实现了减少赫维兹系列中的订单的方法。
In this paper, we first introduce the unlacing of Hurwitz series, which can be viewed as an inverse of interlacing, and develop the basic properties of unlacing, interlacing and integral of Hurwitz series. We then show that the multiplication of interlacing of Hurwitz series by basis elements can be also rewritten as an interlacing, and provide the explicit multiplication formula in terms of integrals and Hadamard products. Finally, we investigate the natural exponential function $\exp$, and realize the method of reduction of order in the ring of Hurwitz series by using $\exp$.
