On the Irreducibility of Extended Bessel Polynomials

We generalize a well-known result proved by Filaseta and Trifonov in 2002 that the Bessel polynomials of all degrees are irreducible over the field of rational numbers. The proof given here of our generalization appears to be simpler than the known proofs of Filaseta-Trifonov Theorem. We use some recent results by Lehmer, Luca, Najman and Shorey regarding the largest prime divisor of a product of consecutive integers, which play a significant role in making the proof shorter. The backbone of our