Mehler–Heine type formulas for Charlier and Meixner polynomials

Dominici, Diego

doi:10.1007/s11139-014-9665-5

Cited by 9 publications

(8 citation statements)

References 66 publications

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“…In a previous work [16], we found the asymptotic zero distribution of polynomial families satisfying first-order differential-recurrence relations of the form (12). It would be interesting to know if our results could be extended to include the polynomials P n (c) studied in this paper.…”

Section: Resultsmentioning

confidence: 71%

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Polynomial Sequences Associated with the Moments of Hypergeometric Weights

Dominici

2016

SIGMA

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Section: Resultsmentioning

confidence: 71%

“…We derived (23) in [12] using a different approach. If we define the Stieltjes transform of P n (c) by…”

Section: Stieltjes Transformmentioning

confidence: 99%

Polynomial Sequences Associated with the Moments of Hypergeometric Weights

Dominici

2016

SIGMA

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“…These identities may be considered as analogues of the properties of the zeros of the Askey scheme and generalized hypergeometric polynomials proved in [12,13,14,15], for the case of the polynomial families considered in this paper. An application of the identities proved in this paper is related to the study of the asymptotic behavior of algebraic expressions involving the zeros of orthogonal polynomials of degree N as N → ∞, see [32,33].…”

Section: Main Result: Algebraic Identities Satisfied By the Zeros Of mentioning

confidence: 97%

Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials

Bihun

Mourning

2018

Advances in Mathematical Physics

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Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived. The generalization is based on a modification of pseudospectral matrix representations of linear differential operators proposed in the paper, which allows these representations to depend on two, rather than one, sets of interpolation nodes. The identities hold for every polynomial family { ] ( )} ∞ ]=0 orthogonal with respect to a measure supported on the real line that satisfies some standard assumptions, as long as the polynomials in the family satisfy differential equations A ] ( ) = ] ( ) ] ( ), where A is a linear differential operator and each ] ( ) is a polynomial of degree at most 0 ∈ N; 0 does not depend on ]. The proposed identities generalize known identities for classical and Krall orthogonal polynomials, to the case of the nonclassical orthogonal polynomials that belong to the class described above. The generalized pseudospectral representations of the differential operator A for the case of the Sonin-Markov orthogonal polynomials, also known as generalized Hermite polynomials, are presented. The general result is illustrated by new algebraic relations satisfied by the zeros of the Sonin-Markov polynomials.

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“…8.1.2,p.192]). There are generalizations to other classical orthogonal polynomials, which are also called the Mehler-Heine formula or Meler-Heine type formula (see [37] for a review).…”

Section: Introductionmentioning

confidence: 99%

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

Ahbli

2021

Preprint

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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.

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Mehler–Heine type formulas for Charlier and Meixner polynomials

Cited by 9 publications

References 66 publications

Polynomial Sequences Associated with the Moments of Hypergeometric Weights

Polynomial Sequences Associated with the Moments of Hypergeometric Weights

Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials

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

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