11.5.2.36 Fourier method

Problem: Find the functions \( u(r, \varphi) \), harmonic outside the circle radius \( r=a \) and satisfying the boundary condition (the first exterior boundary-value for the circle): \[ \left.\frac{\partial u}{\partial r}\right|_{r=a}=A \cos 3 \varphi \text {. } \]