Throughout this paper e denotes an integer ⩾ 3 and p a prime $\equiv 1 (\mod e)$. With f defined by p = ef + 1 and for integers r and s satisfying $1 \leqslant s < r \leqslant e - 1$, certain binomial ...

In this note we give a rigorous proof by elementary means of the asymptotic behavior of the binomial coefficients. As an application we look at the convergence of the binomial series at the endpoints ...