Classical skew orthogonal polynomials in a two-component log-gas with charges +1 and +2

There is a two-component log-gas system with Boltzmann factor which provides an interpolation between the eigenvalue probability density function (PDF) for β=1 and β=4 invariant random matrix ensembles. Its solvability relies on construction of particular skew orthogonal polynomials, inner product linear combination products, each involving weight functions. For suitably related classical functions, we seek to express polynomials as combinations underlying polynomials. It found that in case (Gaussian, Laguerre, Jacobi generalised Cauchy) coefficients can be expressed terms hypergeometric argument relating fugacity. In case, example, are Wilson