On the Galois group of Generalised Laguerre polynomials II

2019/01/04 by Laishram, Shanta, Nair, Saranya G., Shorey, Tarlok Nath
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1901.01066

Abstract

For real number α, Generalised Laguerre Polynomials (GLP) is a family of polynomials defined by L_n^(α)(x)=(-1)ⁿ∑_j=0ⁿ\binomn+αn-j((-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^((1)/(2)+u)(x²) when u is a negative integer.

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