Irreducibility of generalized Hermite–Laguerre polynomials III

Abstract

For a positive integer n and a real number α, the generalized Laguerre polynomials are defined by

Squares in blocks from an arithmetic progression and Galois group of Laguerre polynomials

“…We refer to Finch & Saradha [8] for a more recent proof in the case (u, v) = (1, 2). Laishram and Shorey, in [13], [14], [15] showed that g(x) is irreducible for the rest of the values of (u, v) considered in Theorem 1.4.…”