Show that for all $k$ in $\mathbb { N } ^ { * } , \left| \varphi _ { n } ( x ) \right| = o \left( \frac { 1 } { n ^ { k } } \right)$ as $n$ tends to $+ \infty$. Use Fourier series of successive derivatives of $G _ { x }$.
Show that for all $k$ in $\mathbb { N } ^ { * } , \left| \varphi _ { n } ( x ) \right| = o \left( \frac { 1 } { n ^ { k } } \right)$ as $n$ tends to $+ \infty$.
Use Fourier series of successive derivatives of $G _ { x }$.