Closed-form expressions, generating function and Mehler-Heine type formula for the associated Meixner polynomials and some applications

2021/03/15 by Khalid Ahbli, Ahbli, Khalid
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2103.08367

openalex publication_date 2021/03/15 · openalex created_date 2021/03/29 · openalex updated_date 2026/07/28

Abstract

We give a closed-form expression for the associated Meixner polynomials from which we derive closed-form expressions for the associated Charlier and Laguerre polynomials by a limit procedure. These formulas are then used to derive generating functions of these polynomials. Also, we investigate the Mehler-Heine type asymptotic formulas for the associated Meixner and Charlier polynomials. Some applications and consequences of our results are also mentioned.

Citations

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Explicit Formulas for the Associated Jacobi Polynomials and Some Applications

Related

• Mehler-Heine type formulas for Charlier and Meixner polynomials
• New results on the associated Meixner, Charlier, Laguerre, and Krawtchouk polynomials
• Multivariate Meixner, Charlier and Krawtchouk polynomials
• Asymptotics for Multiple Meixner Polynomials
• Convergent Asymptotic Expansions of Charlier, Laguerre and Jacobi Polynomials