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