On the Galois group of Generalised Laguerre polynomials II
Number Theory
2019-01-07 v1
Abstract
For real number Generalised Laguerre Polynomials (GLP) is a family of polynomials defined by \begin{align*} L_n^{(\alpha)}(x)=(-1)^n\displaystyle\sum_{j=0}^{n}\binom{n+\alpha}{n-j}\frac{(-x)^j}{j!}. \end{align*}These orthogonal polynomials are extensively studied in Numerical Analysis and Mathematical Physics. In 1926, Schur initiated the study of algebraic properties of these polynomials. We consider the Galois group of Generalised Laguerre Polynomials when is a negative integer.
Cite
@article{arxiv.1901.01066,
title = {On the Galois group of Generalised Laguerre polynomials II},
author = {Shanta Laishram and Saranya G. Nair and Tarlok Nath Shorey},
journal= {arXiv preprint arXiv:1901.01066},
year = {2019}
}