grandes-ecoles 2013 QI.B

grandes-ecoles · France · centrale-maths1__psi Sequences and Series Functional Equations and Identities via Series
By expressing $G _ { x } ( - t )$ in terms of $G _ { x } ( t )$, show that for $n$ in $\mathbb { Z } , \varphi _ { n } ( x ) \in \mathbb { R }$. 
By expressing $G _ { x } ( - t )$ in terms of $G _ { x } ( t )$, show that for $n$ in $\mathbb { Z } , \varphi _ { n } ( x ) \in \mathbb { R }$.
Paper Questions
QI.A.1 QI.A.2 QI.B QI.C QI.D QII.A QII.B QII.C.1 QII.C.2 QII.C.3 QII.C.4 QII.D QII.E.1 QII.E.2 QII.E.3 QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.B.1 QIII.B.2 QIII.B.3 QIII.B.4 QIV.A QIV.B QIV.C.1 QIV.C.2 QIV.C.3 QIV.D.1 QIV.D.2