Chapter 14.1, Problem 1E

1. (a) Show that $\text{erf}\left(\sqrt{t}\right)=\frac{1}{\sqrt{\pi }}{\displaystyle {\int }_0^t\frac{e^{-\tau }}{\sqrt{\tau }}d\tau .}$
2. (b) Use part (a), the convolution theorem, and the results of Problem 43 in Exercises 7.1 to show that

     $L\left\{\text{erf}\left(\sqrt{t}\right)\right\}=\frac{1}{s\sqrt{s+1}}$