Interlacing of zeros of linear combinations of classical orthogonal polynomials from different sequences

We prove that the zeros of polynomials of consecutive degree in the sequences {rn}n=1∞ and {sn}n=1∞ are interlacing for n∈N, n⩾1 wherern=pn+anqn,sn=pn+bnqn−1,an,bn≠0,an,bn∈R and {pn}n=1∞ and {qn}n=1∞ are different sequences of Laguerre (respectively Jacobi) polynomials.