  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 $\exp$.
