Hi I'm having troubles with a question and was wondering if someone could guide me through it:

Given two mystery functions called anna and bob. Both have power series representations

that work for all x $\displaystyle \epsilon$ R

Anna(x) = $\displaystyle \sum_{n=0}^{\infty }a_{n}x^{n}$, bob(x)= $\displaystyle \sum_{n=0}^{\infty }b_{n}x^{n}$

Furthermore, anna(0) = 0; bob(0) = 1 and we know that deriving bob gives anna and deriving

anna gives bob.

a) Find anna and bob, i.e. nd the coefficients $\displaystyle a_{n}$ and $\displaystyle b_{n}$ of their power series.

b) Express the exponential function $\displaystyle e^{x}$ and $\displaystyle e^{-x}$ as a combination of anna and bob. Conversely,

express anna and bob as a combination of $\displaystyle e^{x}$ and $\displaystyle e^{-x}$

Thanks in advance