Some identities associated with $2$-variable truncated exponential based Sheffer polynomial sequences
Commun. Korean Math. Soc. 2020 Vol. 35, No. 2, 533-546
https://doi.org/10.4134/CKMS.c190104
Published online April 6, 2020
Junesang Choi, Saima Jabee, Mohd Shadab
Dongguk University; Jamia Millia Islamia (A Central University); Jamia Millia Islamia (A Central University)
Abstract : Since Sheffer introduced the so-called Sheffer polynomials in 1939, the polynomials have been extensively investigated, applied and classified. In this paper, by using matrix algebra, specifically, some properties of Pascal and Wronskian matrices, we aim to present certain interesting identities involving the $2$-variable truncated exponential based Sheffer polynomial sequences. Also, we use the main results to give some interesting identities involving so-called $2$-variable truncated exponential based Miller-Lee type polynomials. Further, we remark that a number of different identities involving the above polynomial sequences can be derived by applying the method here to other combined generating functions.
Keywords : Sheffer polynomials, truncated exponential-Sheffer polynomial sequences, Pascal matrix, Wronskian matrix, Miller-Lee type polynomials
MSC numbers : 15A15, 15A24, 42C05, 65QXX
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