# Table 3 Differential transforms${\mathbit{G}}_{\mathbit{i}}\mathbf{\left(}\mathbit{k}\mathbf{\right)}$for$\mathbit{g}\mathbf{\left(}\mathbit{t}\mathbf{\right)}\mathbf{=}\mathbf{exp}\mathbf{\left[}\mathbit{y}\mathbf{\left(}\mathbit{t}\mathbf{\right)}\mathbf{\right]}$,$\mathbit{k}\mathbf{=}\mathbf{0}\mathbf{,}\mathbf{1}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{3}\mathbf{,}\mathbf{4}$
k ${\mathbit{G}}_{\mathbit{i}}\mathbf{\left(}\mathbit{k}\mathbf{\right)}$
0 $exp\left[{Y}_{i}\left(0\right)\right]$
1 ${Y}_{i}\left(1\right)exp\left[{Y}_{i}\left(0\right)\right]$
2 $\left({\left({Y}_{i}\left(1\right)\right)}^{2}/2+{Y}_{i}\left(2\right)\right)exp\left[{Y}_{i}\left(0\right)\right]$
3 $\left({\left({Y}_{i}\left(1\right)\right)}^{3}/3!+{Y}_{i}\left(1\right){Y}_{i}\left(2\right)+{Y}_{i}\left(3\right)\right)exp\left[{Y}_{i}\left(0\right)\right]$
4 $\left({\left({Y}_{i}\left(1\right)\right)}^{4}/4!+{\left({Y}_{i}\left(1\right)\right)}^{2}{Y}_{i}\left(2\right)/2!+{\left({Y}_{i}\left(2\right)\right)}^{2}/2+{Y}_{i}\left(1\right){Y}_{i}\left(3\right)+{Y}_{i}\left(4\right)\right)exp\left[{Y}_{i}\left(0\right)\right]$