The Recurrence Coefficients of Orthogonal Polynomials with a Weight Interpolating between the Laguerre Weight and the Exponential Cubic Weight

Chao Min () and Pixin Fang
Additional contact information
Chao Min: School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
Pixin Fang: School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Mathematics, 2023, vol. 11, issue 18, 1-11

Abstract: In this paper, we consider the orthogonal polynomials with respect to the weight w ( x ) = w ( x ; s ) : = x λ e − N [ x + s ( x 3 − x ) ] , x ∈ R + , where λ > 0 , N > 0 and 0 ≤ s ≤ 1 . By using the ladder operator approach, we obtain a pair of second-order nonlinear difference equations and a pair of differential–difference equations satisfied by the recurrence coefficients α n ( s ) and β n ( s ) . We also establish the relation between the associated Hankel determinant and the recurrence coefficients. From Dyson’s Coulomb fluid approach, we prove that the recurrence coefficients converge and the limits are derived explicitly when q : = n / N is fixed as n → ∞ .

Keywords: orthogonal polynomials; Laguerre weight; exponential cubic weight; ladder operators; difference equations; Coulomb fluid (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/18/3842/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/18/3842/ (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:11:y:2023:i:18:p:3842-:d:1235158

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 ().