Extension of Laguerre polynomials with negative arguments

We consider the irreducibility of polynomial L n ( α ) x where is a negative integer. observe that constant term vanishes if and only ≥ | = − . Therefore we assume s 1 non-negative Let g ∑ j 0 ! more general polynomial, let G b with ≤ are integers such Schur was first to prove for It has been proved irreducible 60 In this paper, by different method, prove: Apart from finitely many explicitly given possibilities, either or linear factor times polynomial. This consequence estimate > 9 k whenever degree 2 , ≠ 10 5 4 sharpens earlier estimates Shorey Tijdeman Nair Shorey.