The reducibility Of An Airy Operator

Abstract

We show that the determinant $\nabla(d,\alpha),$ which seems to be not considered in the past, is not zero. As an application of this result we prove that the Setoyanagi operator $S_{p,q}=\partial^{2}-(ax^{p}+bx^{q}) $ is irreducible over $\mathbb{C}(x) [ \partial] $.