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On the Galois group of Generalised Laguerre polynomials II

Abstract : 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.
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Submitted on : Friday, May 1, 2020 - 10:14:54 AM
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Shanta Laishram, Saranya G. Nair, T. N. Shorey. On the Galois group of Generalised Laguerre polynomials II. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2020, Volume 42 - Special Commemorative volume in honour of Alan Baker - 2019, pp.26 - 30. ⟨10.46298/hrj.2020.6457⟩. ⟨hal-02554227⟩

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