论文标题
在广义laguerre多项式上的不可约性结果$ l_n^{（ - 1-n-s）}（x）$
Extension of Irreducibility results on Generalised Laguerre Polynomials $L_n^{(-1-n-s)}(x)$
论文作者
论文摘要
我们考虑$ l_n^{（ - 1-n-s）}（x）= \ displayStyle \ sum_ {j = 0}^{n} {n} {n} \ binom {n-j+s} {家庭提供了引起极大兴趣的多项式。早些时候证明，对于$ 0 \ leq s \ leq 60，$这些多项式在$ \ mathbb {q}上都是不可约的。$在本文中，我们将此结果提高到$ s \ leq88。$ $。
We consider the irreducibility of Generalised Laguerre Polynomials for negative integral values given by $L_n^{(-1-n-s)}(x)=\displaystyle\sum_{j=0}^{n}\binom{n-j+s}{n-j}\frac{x^j}{j!}.$ For different values of $s,$ this family gives polynomials which are of great interest. It was proved earlier that for $0 \leq s \leq 60,$ these polynomials are irreducible over $\mathbb{Q}.$ In this paper we improve this result upto $s \leq 88.$
