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EnglishThe 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.
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| Titolo: | Polynomial sequences: elementary basic methods and application hints. A survey | |
| Autori: | NAPOLI, Anna (Corresponding) | |
| Data di pubblicazione: | 2019 | |
| Rivista: | ||
| Handle: | http://hdl.handle.net/20.500.11770/294393 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/20.500.11770/294393
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