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September 2018 Existence of a pair of new recurrence relations for the Meixner-Pollaczek polynomials
E. I. Jafarov, A. M. Jafarova, S. M. Nagiyev
Tbilisi Math. J. 11(3): 29-39 (September 2018). DOI: 10.32513/tbilisi/1538532024

Abstract

We report on existence of pair of new recurrence relations (or difference equations) for the Meixner-Pollaczek polynomials. Proof of the correctness of these difference equations is also presented. Next, we found that subtraction of the forward shift operator for the Meixner-Pollaczek polynomials from one of these recurrence relations leads to the difference equation for the Meixner-Pollaczek polynomials generated via $\cosh$ difference differentiation operator. Then, we show that, under the limit $\varphi \to 0$, new recurrence relations for the Meixner-Pollaczek polynomials recover pair of the known recurrence relations for the generalized Laguerre polynomials. At the end, we introduced differentiation formula, which expresses Meixner-Pollaczek polynomials with parameters $\lambda>0$ and $0 \lt \varphi \lt \pi$ via generalized Laguerre polynomials.

Funding Statement

This work was supported by the Science Development Foundation under the President of the Republic of Azerbaijan Grant Nr EIF-KETPL-2-2015-1(25)-56/01/1 and Grant Nr EIF-KETPL-2-2015-1(25)-56/02/1. E.I. Jafarov kindly acknowledges support for visit to ICTP during July-September 2017, within the ICTP regular associateship scheme.

Citation

Download Citation

E. I. Jafarov. A. M. Jafarova. S. M. Nagiyev. "Existence of a pair of new recurrence relations for the Meixner-Pollaczek polynomials." Tbilisi Math. J. 11 (3) 29 - 39, September 2018. https://doi.org/10.32513/tbilisi/1538532024

Information

Received: 15 November 2017; Accepted: 15 June 2018; Published: September 2018
First available in Project Euclid: 3 October 2018

zbMATH: 07172273
MathSciNet: MR3954192
Digital Object Identifier: 10.32513/tbilisi/1538532024

Subjects:
Primary: 33C45
Secondary: 39A10, 42C05

Rights: Copyright © 2018 Tbilisi Centre for Mathematical Sciences

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Vol.11 • No. 3 • September 2018
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