Some Polynomial Systems Associated with a Certain Family of Differential Operators

Chen, Kung-Yu; Chyan, Chuan Jen; Srivástava, H. M.

doi:10.1006/jmaa.2002.7922

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Cited by 4 publications

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“…There have been many studies on polynomials via the Rodrigues formula [3][4][5][6][7] and new papers constantly coming out related with these generalizations [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Some properties of generalized multiple Hermite polynomials

Kaanoğlu¹,

Özarslan²

2011

Journal of Computational and Applied Mathematics

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a b s t r a c tThe purpose of this paper is to introduce and discuss a more general class of multiple Hermite polynomials. In this work, the explicit forms, operational formulas and a recurrence relation are obtained. Furthermore, we derive several families of bilinear, bilateral and mixed multilateral finite series relationships and generating functions for the generalized multiple Hermite polynomials.

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“…There have been many studies on polynomials via the Rodrigues formula [3][4][5][6][7] and new papers constantly coming out related with these generalizations [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Some properties of generalized multiple Hermite polynomials

Kaanoğlu¹,

Özarslan²

2011

Journal of Computational and Applied Mathematics

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A new summation identity for the Srivastava–Singhal polynomials

Chen¹

2004

Journal of Mathematical Analysis and Applications

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In his recent investigations involving differential operators for some generalizations of the classical Laguerre polynomials, H. Bavinck [J. Phys. A Math. Gen. 29 (1996) L277-L279] encountered and proved a certain summation identity for the classical Laguerre polynomials. The main object of this sequel to Bavinck's work is to prove a generalization of this summation identity for the Srivastava-Singhal polynomials. The demonstration, which is presented here in the general case, differs markedly from the earlier proof given for the known special case. It is also indicated how the general summation identity can be applied to derive the corresponding result for one class of the Konhauser biorthogonal polynomials.  2004 Elsevier Inc. All rights reserved.

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