grandes-ecoles 2025 Q29

grandes-ecoles · France · centrale-maths2__official Sequences and Series Functional Equations and Identities via Series

Show that, for all $t \in \mathbb{R}$, $$\sum_{x \in \Lambda_n} \prod_{i=1}^n \mathrm{e}^{(t+h)x_i} = (2\operatorname{ch}(t+h))^n$$

Show that, for all $t \in \mathbb{R}$,
$$\sum_{x \in \Lambda_n} \prod_{i=1}^n \mathrm{e}^{(t+h)x_i} = (2\operatorname{ch}(t+h))^n$$