Distribution of the Zeros of Jacobi Polynomials Associated with Varying Weights

We introduce a new class of Jacobi polynomials orthogonal with respect to certain varying weights. Using the WKB(Wenttzel-Kramers-Brillouin) approximation method, we analyze the distribution of the zeros of the polynomials. Furthermore, we determine explicitly the asymptotic behavior of the zeros when both degree n of polynomials and a relativistic parameter N approach infinity using potential theory techniques.