grandes-ecoles 2013 QI.C.2

grandes-ecoles · France · centrale-maths1__pc Sequences and Series Functional Equations and Identities via Series
Let $p$ be the function from $\mathbb { R }$ to $\mathbb { R }$ defined by $$p ( x ) = \sum _ { n = 1 } ^ { + \infty } \frac { \cos ( n x ) } { n \sqrt { n } }$$
Determine the Fourier series of $p$.
Let $p$ be the function from $\mathbb { R }$ to $\mathbb { R }$ defined by
$$p ( x ) = \sum _ { n = 1 } ^ { + \infty } \frac { \cos ( n x ) } { n \sqrt { n } }$$

Determine the Fourier series of $p$.