1 1 h (t) = h(0)+ h′(0)t+ ⋅⋅⋅+ --hk(0)tk +-------h(k+1)(s)tk+1,|s| < |t| k! (k+ 1)!
( ) P (u + v) = P (u )+ DP (u)v+-1D2P (u)(v,v)+ ⋅⋅⋅+ 1-DkP (u)(v,⋅⋅⋅,v)+ o |v|k 2! k!
Now you can use the representation theorem Theorem 18.12.14 to write this in the following form.