Hardy Ramanujan Journal |

For real number $\alpha,$ Generalised Laguerre Polynomials (GLP) is a family of polynomials defined by$$L_n^{(\alpha)}(x)=(-1)^n\displaystyle\sum_{j=0}^{n}\binom{n+\alpha}{n-j}\frac{(-x)^j}{j!}.$$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 $L_n^{(\frac{1}{2}+u)}(x)$ when $u$ is a negative integer.

Source : oai:HAL:hal-02554227v1

Volume: Volume 42 - Special Commemorative volume in honour of Alan Baker - 2019

Published on: May 20, 2020

Submitted on: May 7, 2020

Keywords: [MATH]Mathematics [math],[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]

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