The present paper contains a small survey on the principal and elementary methods for a systematic study of general polynomial sequences. For the set of polynomial sequences the algebraic structure of a group is given. Matricial forms, recurrence relations and conjugate sequences of polynomials are examined. For every element of a polynomial sequence determinant forms are determined by suitable Hessenberg matrices. Generating functions and derivation matrix are derived. Then, associated differential operator and Sheffer classification are considered. As an application, a general interpolation problem is hinted at. For a real valued function, the generalized Taylor polynomial and series are given. As an illustrative example, the shifted (with respect to the degree) Fibonacci polynomial sequence is considered.

Polynomial sequences: elementary basic methods and application hints. A survey

Costabile F. A.;Gualtieri M. I.;Napoli A.
2019

Abstract

The present paper contains a small survey on the principal and elementary methods for a systematic study of general polynomial sequences. For the set of polynomial sequences the algebraic structure of a group is given. Matricial forms, recurrence relations and conjugate sequences of polynomials are examined. For every element of a polynomial sequence determinant forms are determined by suitable Hessenberg matrices. Generating functions and derivation matrix are derived. Then, associated differential operator and Sheffer classification are considered. As an application, a general interpolation problem is hinted at. For a real valued function, the generalized Taylor polynomial and series are given. As an illustrative example, the shifted (with respect to the degree) Fibonacci polynomial sequence is considered.
Derivation matrix, Determinant forms, Fibonacci polynomials, Generating functions, Polynomial sequences
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/294393
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