A Riemann-Hilbert problem for Jacobi-Pineiro orthogonal polynomials

We investigate the asymptotic behaviour of Jacobi-Pineiro polynomials of degree $2n$ orthogonal on $[0,1]$ with respect to weights $w_j(x) = x^{\alpha_j}(1-x)^{\beta}$, $j=1,2$ where $\alpha_1,\alpha_2, \beta>-1$, and $\alpha_1-\alpha_2\in (0,1)$. These polynomials are characterized by a Riemann-Hilbert problem for a $3 \times 3$ matrix valued function. We use the Deift-Zhou steepest descent method for Riemann-Hilbert problems to obtain strong uniform asymptotics in the complex plane. The local parametrix around the origin is constructed using Meijer G-functions. We match the local parametrix around the origin with the global parametrix with a double matching, a technique that was recently introduced.