\[\operatorname{Bi}\left(z\right)=\operatorname{Bi}\left(0\right)\left(1+\frac{1%
}{3!}z^{3}+\frac{1\cdot 4}{6!}z^{6}+\frac{1\cdot 4\cdot 7}{9!}z^{9}+\cdots%
\right)+\operatorname{Bi}'\left(0\right)\left(z+\frac{2}{4!}z^{4}+\frac{2\cdot
5%
}{7!}z^{7}+\frac{2\cdot 5\cdot 8}{10!}z^{10}+\cdots\right),\]