In this paper the set of general polynomial sequences is considered. An elementary systematic approach is proposed. In fact a structure of group is given and for every element of this group recurrence relations and determinant forms are derived. Applications of the derived determinant forms are considered. In particular, the general linear interpolation and bounds of the zeros of each polynomial of the sequence are sketched. Finally, as an illustrative example, the shifted (with respect to the degree) Genocchi polynomial sequence is analyzed.

Recurrence relations and determinant forms for general polynomial sequences. Application to Genocchi polynomials

Francesco A. Costabile;Anna Napoli;Maria I. Gualtieri
2019

Abstract

In this paper the set of general polynomial sequences is considered. An elementary systematic approach is proposed. In fact a structure of group is given and for every element of this group recurrence relations and determinant forms are derived. Applications of the derived determinant forms are considered. In particular, the general linear interpolation and bounds of the zeros of each polynomial of the sequence are sketched. Finally, as an illustrative example, the shifted (with respect to the degree) Genocchi polynomial sequence is analyzed.
Polynomial sequences, determinant forms, derivation matrix, Genocchi polynomials
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/288666
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