grandes-ecoles 2013 QIII.B.1

grandes-ecoles · France · centrale-maths1__pc Sequences and Series Functional Equations and Identities via Series

Let $x \in ] - 1,1 [$.
Determine the Fourier series of the function $\widetilde { h } : \mathbb { R } \rightarrow \mathbb { R }$ defined by $\widetilde { h } ( \theta ) = \ln \left( x ^ { 2 } - 2 x \cos \theta + 1 \right)$.
One may use the result from question II.A.2.

Let $x \in ] - 1,1 [$.

Determine the Fourier series of the function $\widetilde { h } : \mathbb { R } \rightarrow \mathbb { R }$ defined by $\widetilde { h } ( \theta ) = \ln \left( x ^ { 2 } - 2 x \cos \theta + 1 \right)$.

One may use the result from question II.A.2.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.B.1 QI.B.2 QI.C.1 QI.C.2 QI.C.3 QII.A.1 QII.A.2 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QII.C.1 QII.C.2 QII.C.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 QIII.B.5 QIII.B.6 QIII.C.1 QIII.C.2 QIII.C.3 QIII.C.4 QIII.D.1 QIII.D.2 QIII.D.3 QIII.D.4 QIII.D.5 QIII.D.6 QIII.D.7 QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.B QIV.C.1 QIV.C.2