Differential equation for Jacobi-Pineiro polynomials

For $r\in {\mathbb{Z}}_{\ge 0}$, we present a linear differential operator %$(\text{di}{)}^{r+1}+a_1(x)(\text{di}{)}^r+\mathrm{.}\mathrm{.}\mathrm{.}+a_{r+1}(x)$ of order $r+1$ with rational coefficients and depending on parameters. This operator annihilates the $r$-multiple Jacobi-Pi~neiro polynomial. For integer values of parameters satisfying suitable inequalities, it is the unique Fuchsian operator with kernel consisting of polynomials only and having three singular points at $x=0, 1, \infty$witharbitrarynon-negativeintegerexponents$0, m_1+1, >…, m_1+…+m_r+r$at$x=0$,specialexponents$0, k+1, k+2,…, k+r$at$x=1$ and arbitrary exponents at $x=\mathrm{\infty }$.