Extension of Laguerre polynomials with negative arguments II

2021/10/16 by T. N. Shorey, Shorey, T. N., Sneh Bala Sinha +1
Mathematics · Physics and Astronomy · #11A41 #11B25 #11C08 #11N05 #11N13 #11Z05 #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.08587

openalex publication_date 2021/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For n ≥ 3 and s ≤ 92, it is proved in \citeShSi that, except for finitely many pairs (n, s), G₁(x) = G₁(x, n, s) is either irreducible or linear factor times an irreducible polynomial. If s ≤ 30, we determine here explicitely the set of pairs (n, s) in the above assertion. This implies a new proof of the result of Nair and Shorey \citeNaSh1 that G₁(x) is irreducible for s ≤ 22.

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