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 R

Anna(x) = , bob(x)=

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 and of their power series.

b) Express the exponential function and as a combination of anna and bob. Conversely,

express anna and bob as a combination of and

Thanks in advance :)