grandes-ecoles 2013 QII.C.1

grandes-ecoles · France · centrale-maths1__pc Sequences and Series Functional Equations and Identities via Series
Let $r : \mathbb { R } \rightarrow \mathbb { R }$, be a $2 \pi$-periodic, odd function, such that $\forall \theta \in ] 0 , \pi ] , r ( \theta ) = \frac { \pi - \theta } { 2 }$.
Justify the existence and uniqueness of $r$.
Let $r : \mathbb { R } \rightarrow \mathbb { R }$, be a $2 \pi$-periodic, odd function, such that $\forall \theta \in ] 0 , \pi ] , r ( \theta ) = \frac { \pi - \theta } { 2 }$.

Justify the existence and uniqueness of $r$.