grandes-ecoles 2022 Q3

grandes-ecoles · France · mines-ponts-maths1__psi Sequences and Series Properties and Manipulation of Power Series or Formal Series

Let $z \in D$. Show that the function $\Psi : t \mapsto (1-tz)e^{L(tz)}$ is constant on $[0,1]$, and deduce that $$\exp(L(z)) = \frac{1}{1-z}$$

Let $z \in D$. Show that the function $\Psi : t \mapsto (1-tz)e^{L(tz)}$ is constant on $[0,1]$, and deduce that
$$\exp(L(z)) = \frac{1}{1-z}$$