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Bessel polynomials and the partial sums of the exponential series. (English) Zbl 1238.05007
Summary: Let ε k (x) denote the kth partial sum of the Maclaurin series for the exponential function. Define the (n+1)×(n+1) Hankel determinant by setting H ˜ n (x)=det[e i+j (x)] 0i,jn . We give a closed form evaluation of this determinant in terms of the Bessel polynomials using the method of recently introduced γ-operators.
MSC:
05A10Combinatorial functions
05A15Exact enumeration problems, generating functions
05A19Combinatorial identities, bijective combinatorics
11C20Matrices, determinants (number theory)
33C45Orthogonal polynomials and functions of hypergeometric type