General Odd and Even Central Factorial Polynomial Sequences

Costabile, Francesco Aldo; Gualtieri, Maria Italia; Napoli, Anna

doi:10.3390/math10060978

Open AccessArticle

General Odd and Even Central Factorial Polynomial Sequences

by

Francesco Aldo Costabile

^*,

Maria Italia Gualtieri

and

Anna Napoli

Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy

^*

Author to whom correspondence should be addressed.

Mathematics 2022, 10(6), 978; https://doi.org/10.3390/math10060978

Submission received: 22 February 2022 / Revised: 15 March 2022 / Accepted: 16 March 2022 / Published: 18 March 2022

(This article belongs to the Special Issue Polynomial Sequences and Their Applications)

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Abstract

The

δ^{2} (\cdot)

operator, where

δ (\cdot)

is the known central difference operator, is considered. The associated odd and even polynomial sequences are determined and their generalizations studied. Particularly, matrix and determinant forms, recurrence formulas, generating functions and an algorithm for effective calculation are provided. An interesting property of biorthogonality is also demonstrated. New examples of odd and even central polynomial sequences are given.

Keywords: polynomial sequences; central factorial polynomials; odd and even polynomials; discrete operators; Hessenberg determinant; recurrence

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MDPI and ACS Style

Costabile, F.A.; Gualtieri, M.I.; Napoli, A. General Odd and Even Central Factorial Polynomial Sequences. Mathematics 2022, 10, 978. https://doi.org/10.3390/math10060978

AMA Style

Costabile FA, Gualtieri MI, Napoli A. General Odd and Even Central Factorial Polynomial Sequences. Mathematics. 2022; 10(6):978. https://doi.org/10.3390/math10060978

Chicago/Turabian Style

Costabile, Francesco Aldo, Maria Italia Gualtieri, and Anna Napoli. 2022. "General Odd and Even Central Factorial Polynomial Sequences" Mathematics 10, no. 6: 978. https://doi.org/10.3390/math10060978

APA Style

Costabile, F. A., Gualtieri, M. I., & Napoli, A. (2022). General Odd and Even Central Factorial Polynomial Sequences. Mathematics, 10(6), 978. https://doi.org/10.3390/math10060978

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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General Odd and Even Central Factorial Polynomial Sequences

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