a bound using cauchy formulea

let $ 0<t_0<1$ fixed number , $ n_0$ integer $ \geq 2$ fixed and let $ \forall 0<u<1, f(u)= \displaystyle \frac{(1-u)^n \log(1-u)}{(1-ut_0)^{n+1}} $ . let $ 0<u_0<1 $ fixe real….