English

On the Galois group of Generalised Laguerre polynomials II

Number Theory 2019-01-07 v1

Abstract

For real number α,\alpha, 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 Ln(12+u)(x2) L_n^{(\frac{1}{2}+u)}(x^2) when uu is a negative integer.

Keywords

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}
}