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April 2019 Product of Sheffer sequences: properties and examples
Mumtaz Riyasat, Subuhi Khan, Shakir Shah
Tbilisi Math. J. 12(2): 101-118 (April 2019). DOI: 10.32513/tbilisi/1561082571


This article is written with an objective to explore the product of two Sheffer sequences. This article is an attempt to explore such type of product which extends the possibility to consider hybrid type Sheffer polynomials. It is important to remark that although this product can be viewed as the umbral composition of two Sheffer sequences but the results related to this product cannot be deduced from the results of the Sheffer sequences. The set of this product of Sheffer sequences is also a non-abelian group and thus convoluting different members of Sheffer class allows us to consider a number of hybrid type special polynomials as its members. Certain results for this class including the quasi-monomiality and determinant form are established. The article concludes with the possibility of considering the product of $n$-Sheffer sequences.

Funding Statement

This work has been done under Post-Doctoral Fellowship (Office Memo No.2/40(38)/2016/R$\&$D-II/1063) awarded to Mumtaz Riyasat by the National Board of Higher Mathematics, Department of Atomic Energy, Government of India, Mumbai.


Download Citation

Mumtaz Riyasat. Subuhi Khan. Shakir Shah. "Product of Sheffer sequences: properties and examples." Tbilisi Math. J. 12 (2) 101 - 118, April 2019.


Received: 22 September 2018; Accepted: 10 April 2019; Published: April 2019
First available in Project Euclid: 21 June 2019

zbMATH: 07172316
MathSciNet: MR3973263
Digital Object Identifier: 10.32513/tbilisi/1561082571

Primary: 11B83
Secondary: 11C20, 12E10

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences


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Vol.12 • No. 2 • April 2019
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