Odd and even Lidstone-type polynomial sequences. Part 1: basic topics

Two new general classes of polynomial sequences called respectively odd and even Lidstone-type polynomials are considered. These classes include classic Lidstone polynomials of first and second kind. Some characterizations of the two classes are given, including matrix form, conjugate sequences, gen...

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Bibliographic Details
Published in:	Advances in difference equations Vol. 2018; no. 1; pp. 1 - 26
Main Authors:	Costabile, F. A., Gualtieri, M. I., Napoli, A., Altomare, M.
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 29-08-2018 Springer Nature B.V SpringerOpen
Subjects:	Analysis Difference and Functional Equations Functional Analysis Infinite matrices Lidstone polynomials Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Polynomial sequences Polynomials Sequences 41A58 Polynomial sequences 11B83 Infinite matrices Lidstone polynomials
Online Access:	Get full text
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Summary:	Two new general classes of polynomial sequences called respectively odd and even Lidstone-type polynomials are considered. These classes include classic Lidstone polynomials of first and second kind. Some characterizations of the two classes are given, including matrix form, conjugate sequences, generating function, recurrence relations, and determinant forms. Some examples are presented and some applications are sketched.
ISSN:	1687-1847 1687-1839 1687-1847
DOI:	10.1186/s13662-018-1733-5