3. The v-Umbral Algebra

1988 ◽  
pp. 12-17
Author(s):  
Frank M. Cholewinski
Keyword(s):  
Umbral Algebra

scholarly journals Some results for Apostol-type polynomials associated with umbral algebra

2013 ◽  
Vol 2013 (1) ◽  
pp. 201 ◽  
Author(s):  
Da-Qian Lu ◽  
Chang-He Xiang ◽  
Qiu-Ming Luo
Keyword(s):  
Umbral Algebra

scholarly journals Some Hermite base polynomials on q-umbral algebra

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 961-967 ◽  
Author(s):  
Rahime Dere
Keyword(s):  
Bernoulli Polynomials ◽  
Umbral Calculus ◽  
New Type ◽  
Umbral Algebra

The aim of this paper is to investigate the q-Hermite type polynomials by using umbral calculus methods. Using this method, we derive new type polynomials which are related to the q-Bernoulli polynomials and the q-Hermite type polynomials. Furthermore, we also derive some new identities of those polynomials which are derived from q-umbral calculus.

scholarly journals On λ-linear functionals arising from p-adic integrals on $\mathbb{Z}_{p}$

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dae San Kim ◽  
Taekyun Kim ◽  
Jongkyum Kwon ◽  
Si-Hyeon Lee ◽  
Seongho Park
Keyword(s):  
Generating Function ◽  
Bernoulli Polynomials ◽  
Linear Functionals ◽  
Invariant Integral ◽  
Umbral Algebra

AbstractThe aim of this paper is to determine the λ-linear functionals sending any given polynomial $p(x)$ p ( x ) with coefficients in $\mathbb{C}_{p}$ C p to the p-adic invariant integral of $P(x)$ P ( x ) on $\mathbb{Z}_{p}$ Z p and also to that of $P(x_{1}+\cdots +x_{r})$ P ( x 1 + ⋯ + x r ) on $\mathbb{Z}_{p}^{r}$ Z p r . We show that the former is given by the generating function of degenerate Bernoulli polynomials and the latter by that of degenerate Bernoulli polynomials of order r. For this purpose, we use the λ-umbral algebra which has been recently introduced by Kim and Kim (J. Math. Anal. Appl. 493(1):124521 2021).

Genocchi polynomials associated with the Umbral algebra

2011 ◽  
Vol 218 (3) ◽  
pp. 756-761 ◽  
Author(s):  
Rahime Dere ◽  
Yilmaz Simsek
Keyword(s):  
Genocchi Polynomials ◽  
Umbral Algebra

scholarly journals Applications of Umbral Calculus Associated withp-Adic Invariant Integrals onZp

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Dae San Kim ◽  
Taekyun Kim
Keyword(s):  
Special Functions ◽  
Bernoulli Polynomials ◽  
Umbral Calculus ◽  
Invariant Integrals ◽  
Umbral Algebra

Recently, Dere and Simsek (2012) have studied the applications of umbral algebra to some special functions. In this paper, we investigate some properties of umbral calculus associated withp-adic invariant integrals onZp. From our properties, we can also derive some interesting identities of Bernoulli polynomials.

Remarks on the Frobenius-Euler polynomials on the umbral algebra

2012 ◽  
Author(s):  
Rahime Dere ◽  
Yilmaz Simsek
Keyword(s):  
Euler Polynomials ◽  
Umbral Algebra

scholarly journals Hermite base Bernoulli type polynomials on the umbral algebra

2015 ◽  
Vol 22 (1) ◽  
pp. 1-5 ◽  
Author(s):  
R. Dere ◽  
Y. Simsek
Keyword(s):  
Umbral Algebra
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