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Zbl 1238.05007
Eğecioğlu, Ömer
Bessel polynomials and the partial sums of the exponential series. (English)
[J] SIAM J. Discrete Math. 24, No. 4, 1753-1762 (2010). ISSN 0895-4801; ISSN 1095-7146/e

Summary: Let $\varepsilon_k(x)$ denote the $k$th partial sum of the Maclaurin series for the exponential function. Define the $(n+ 1)\times(n+ 1)$ Hankel determinant by setting $\widetilde H_n(x)= \text{det}[e_{i+j}(x)]_{0\le i,j\le n}$. We give a closed form evaluation of this determinant in terms of the Bessel polynomials using the method of recently introduced $\gamma$-operators.

MSC 2000:: *05A10 Combinatorial functions
05A15 Combinatorial enumeration problems
05A19 Combinatorial identities
11C20 Matrices, determinants
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: Bessel polynomials; exponential series; Hankel determinants

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