Tricomi Continuants

Emanuele Munarini ()
Additional contact information
Emanuele Munarini: Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

Mathematics, 2024, vol. 12, issue 3, 1-23

Abstract: In this paper, we introduce and study the Tricomi continuants, a family of tridiagonal determinants forming a Sheffer sequence closely related to the Tricomi polynomials and the Laguerre polynomials. Specifically, we obtain the main umbral operators associated with these continuants and establish some of their basic relations. Then, we obtain a Turan-like inequality, some congruences, some binomial identities (including a Carlitz-like identity), and some relations with the Cayley continuants. Furthermore, we show that the infinite Hankel matrix generated by the Tricomi continuants has an LDU-Sheffer factorization, while the infinite Hankel matrix generated by the shifted Tricomi continuants has an LTU-Sheffer factorization. Finally, by the first factorization, we obtain the linearization formula for the Tricomi continuants and its inverse.

Keywords: exponential Riordan matrices; Sheffer polynomials; umbral operators; congruences; binomial identities; Cayley continuants; Hankel matrices; Sheffer factorizations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/3/401/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/3/401/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:3:p:401-:d:1326911

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().