Topic
Sheffer sequence
About: Sheffer sequence is a research topic. Over the lifetime, 173 publications have been published within this topic receiving 3075 citations. The topic is also known as: poweroid.
Papers published on a yearly basis
Papers
TL;DR: The Sheffer group of all Sheffer-type polynomials is defined and the isomorphism between the sheffer group and the Riordan group is proved.
87 citations
TL;DR: From applications of umbral calculus on fermionic p -adic integral on Z p, some new identities on Genocchi numbers and polynomials are derived.
82 citations
TL;DR: In this article, the authors introduced Hermite-based Appell polynomials and investigated the possibility of extending this technique to introduce Hermite based Sheffer polynomorphisms (for example, Hermite Laguerre and Hermite Sister Celine's polynomial).
70 citations
TL;DR: In this paper, the Hermite-based Appell polynomials were derived via the factorization method, and the corresponding equations for Hermite based Bernoulli poynomials and Hermite base Euler polynomial were derived.
Abstract: Recently, Khan { \it et al .} [S. Khan, G. Yasmin , R. Khan and N. A. M. Hassan , Hermite-based Appell polynomials: Properties and Applications, { \it J. Math. Anal. Appl .} { \bf 351} (2009), 756--764] defined the Hermite-based Appell polynomials by \begin {align*} \mathcal G(x,y,z;t)&:=A(t)\exp (xt+yt^{2}+zt^{3})\\ &\;=\sum_{n=0}^{\infty}\; _{H}A_{n}(x,y,z)\;\frac{t^{n}}{n!} \end {align*} and investigated their many interesting properties and characteristics by using operational techniques combined with the principle of monomiality . Here, in this paper, we find the differential, integro -differential and partial differential equations for the Hermite-based Appell polynomials via the factorization method. Furthermore, we derive the corresponding equations for the Hermite-based Bernoulli polynomials and the Hermite-based Euler polynomials. We also indicate how to deduce the corresponding results for the Hermite-based Genocchi polynomials from those involving the Hermite-based Euler polynomials.
58 citations
TL;DR: In this paper, a systemic study of the class of Sheffer sequences in connection with generating function of the weighted q -Euler polynomials is given in the present paper.
53 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 2 |
| 2019 | 4 |
| 2018 | 1 |
| 2017 | 6 |
| 2016 | 11 |