On the constructive solution of an inverse Sturm-Liouville problem

The necessary and sufficient conditions are found for the two sequences ${\left\{{\mu }_n\right\}}_{n=0}^{\mathrm{\infty }}$ and ${\left\{a_n\right\}}_{n=0}^{\mathrm{\infty }}$ to be the spectrum and the norming constants respectively, for a boundary value problem $-y^{\mathrm{\prime }\mathrm{\prime }}+q\left(x\right)y=\mu y,$ $y\left(0\right)=0,$ $y\left( \pi \right)\cos \beta + y’\left( \pi \right)\sin \beta = 0,$ $\beta \in \left( 0, \pi \right),$with$q \in L_{$\mathbb{R}$}^1 \left[0, \pi \right].$