Shanta Laishram ; Saranya G. Nair ; T. N. Shorey - On the Galois group of Generalised Laguerre polynomials II

hrj:6457 - Hardy-Ramanujan Journal, May 20, 2020, Volume 42 - Special Commemorative volume in honour of Alan Baker - https://doi.org/10.46298/hrj.2020.6457
On the Galois group of Generalised Laguerre polynomials II

Authors: Shanta Laishram ; Saranya G. Nair ; T. N. Shorey

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.


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