Extension of Irreducibility results on Generalised Laguerre Polynomials L_n^(-1-n-s)(x)

2022/03/01 by Saranya G. Nair, Nair, Saranya G, T. N. Shorey +1
Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2203.00248

openalex publication_date 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the irreducibility of Generalised Laguerre Polynomials for negative integral values given by L_n^(-1-n-s)(x)=∑_j=0ⁿ\binomn-j+sn-j(x^j)/(j!). For different values of s, this family gives polynomials which are of great interest. It was proved earlier that for 0 ≤ s ≤ 60, these polynomials are irreducible over ℚ. In this paper we improve this result upto s ≤ 88.

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