Let the function z} be defined by ) = 1 and x} = % for: 7E El. One can show that the function f is infinitely man):r times differentiable and that f equals to its Taylor series about 3 = 0. Consider the function t e2 1 y(t) = f dz. 0 2 Then the power series representation of 9(t) about t = 0 is Z a": (t): k=1 where 111:0) =|