I ( x ) = − ∑ s = 0 2 n ( a s ln x + b s ) x − s + O ( x − 2 n − 1 + ε ) I(x)=-\sum_{s=0}^{2n}(a_{s}\ln x+b_{s})x^{-s}+O\left(x^{-2n-1+\epsilon}\right)