Interlacing Properties of Real Zeros of General Laguerre Polynomials

L (↵) n (x) for arbitrary real ↵. Such results are well-known in the case ↵ > 1. In the case 2 < ↵ < 1, we use a mixed 3-term recurrence relation to show, for example, that, apart from a single value of ↵, the (all real) zeros of (x + ↵ + 1)L n (x) interlace with those of xL n (x). By studying the changes in interlacing that occur when ↵ decreases through the negative integer values 1, 2, . . . , we prove similar interlacing results for the zeros of Laguerre polynomials for values of ↵ < 2.