I am studying the generalisation of the Selberg's integral by using Jack polynomial as outlined by Forrester and Warnaar ([arXiv: 0710.3981](https://arxiv.org/abs/0710.3981)). They write down the *symmetric* Jack polynomial as 
\begin{equation}
P\_\lambda^{(\alpha)} = m\_\lambda + \sum\_{\mu < \lambda}a\_{\lambda \mu} m\_\mu
\end{equation}
where $m\_\lambda$ is the monomial symmetric function for the partition $\lambda$. I basically want to play around with the equation number (2.46) in the reference mentioned above. Could someone give me examples of simple Jack polynomials? Also, I don't understand the significance of the parameter $\alpha$ in $P\_\lambda^{(\alpha)}$.



Jack polynomial and Selberg integral
Try this set of notes on the Jack symmetric functions / polynomials: <https://tcjpn.wordpress.com/2016/11/27/a-note-on-the-jack-symmetric-functions-polynomials/>


