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A determinantal approach to Appell polynomials. (English) Zbl 1200.33020
Families of Appell polynomials \((A_n(x))_{n\geq 0}\) satisfy \(\frac{\mathrm{d} A_n(x)}{\mathrm{d} x}=n A_{n-1}(x)\) for \(n\geq 1\). In the present paper a way is presented to express Appell polynomials as certain determinants. From this representation (and by using some linear algebra) the authors get several general properties of Appell polynomials such as recurrences, addition and multiplication theorems, forward differences and symmetry properties. An automated way is presented how to get the coefficients of these polynomials. In the final section, some classical examples of Appell polynomials are revisited.

33C65 Appell, Horn and Lauricella functions
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
11B83 Special sequences and polynomials
65F40 Numerical computation of determinants
Full Text: DOI
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