For integers $a_0,a_1,\ldots,a_n$ with $|a_0a_n|=1$ and either $��=u$ with $1\leq u \leq 50$ or $��=u+ \frac{1}{2}$ with $1 \leq u \leq 45$, we prove that $��_n^{(��)}(x;a_0,a_1,\cdots,a_n)$ is irreducible except for an explicit finite set of pairs $(u,n)$. Furthermore all the exceptions other than $n=2^{12},��=89/2$ are necessary. The above result with $0\leq��\leq 10$ is due to Filaseta, Finch and Leidy and with $��\in \{-1/2,1/2\}$ due to Schur.