A note on the distance between two consecutive zeros of m-orthogonal polynomials for a generalized Jacobi weight

Let xkn=cosθkn,0≤θkn≤π,k=1,2,…,n, with-1=x0n-1,i=1,2,…,r.This note proves θkn-θk+1,n∼1/n,k=0,1,…,n. The gap left over pi<0,2≤i≤r-1, is filled.