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arXiv · 1901.01072

Irreducibility of extensions of Laguerre Polynomials

Shanta Laishram·Saranya G. Nair·Tarlok Nath Shorey
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Abstract

For integers $a_0,a_1,\ldots,a_n$ with $|a_0a_n|=1$ and either $α=u$ with $1\leq u \leq 50$ or $α=u+ \frac{1}{2}$ with $1 \leq u \leq 45$, we prove that $ψ_n^{(α)}(x;a_0,a_1,\cdots,a_n)$ is irreducible except for an explicit finite set of pairs $(u,n)$. Furthermore all the exceptions other than $n=2^{12},α=89/2$ are necessary. The above result with $0\leqα\leq 10$ is due to Filaseta, Finch and Leidy and with $α\in \{-1/2,1/2\}$ due to Schur.

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Shanta Laishram, Saranya G. Nair, Tarlok Nath Shorey. 2019-01-04. Irreducibility of extensions of Laguerre Polynomials. https://arxiv.org/abs/1901.01072

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