A determinantal approach to Sheffer–Appell polynomials via monomiality principle
Copyright policy )A determinantal approach to Sheffer–Appell polynomials via monomiality principle
The authors have combined the Appell and Sheffer polynomials to introduce Sheffer-Appell polynomials by means of generating function, series definition and determinantal definition. Since any sequence of polynomials is quasi-monomial [\textit{Y. Ben Cheikh}, Appl. Math. Comput. 141, No. 1, 63--76 (2003; Zbl 1041.33008)], the quasi-monomiality operators are determined in order to derive some properties of these polynomials. Further, the Sheffer-Bernoulli and Sheffer-Euler polynomials are obtained as particular cases of Sheffer-Appell polynomials. The definitions of the Hermite-Appell polynomials as well as the Laguerre-Appell polynomials are also pointed out.
Appell, Horn and Lauricella functions, Sheffer-Appell polynomials, determinantal definition, quasi-monomiality principle
Appell, Horn and Lauricella functions, Sheffer-Appell polynomials, determinantal definition, quasi-monomiality principle
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