3.

(a) (x2 -l)eX = -1 - x I:~=2(k2 - k - l)xk /k!.

(b) eX cos x = I:~=o(I:jEAk(-1)j/((2j)!(k - 2j)!))· Xk, where Ak := {j EN:

o :S j :S k/2}.

(c) sin x/ex = I:~=l (I:jEA k (_.1)k- j+1 /((2j + l)!(k - 2j -I)!))· xk, where Ak :=

{j EN: 0 :S j :S (k - 1)/2}.

(d) f(x) = I:~=o xk logk+l a/(k + I)!.