BESSEL POLYNOMIALS AND THE PARTIAL SUMS OF THE EXPONENTIAL SERIES ∗

Abstract. Let ek(x) denotethek-th partial sum of the Maclaurin series for the exponential function. Define the (n +1) × (n + 1) Hankel determinant by setting ˜Hn(x) =det[ei+j(x)]0≤i,j≤n. We give a closed form evaluation of this determinant in terms of the Bessel polynomials using the method of recently introduced γ-operators