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Some new identities for the Apostol-Bernoulli polynomials and the Apostol-Genocchi polynomials
(ELSEVIER SCIENCE INC, 2015-07-01)
In this paper, we present a further investigation for the Apostol-Bernoulh polynomials and the Apostol-Genocchi polynomials. By making use of the generating function methods and summation transform techniques, we establish ...
On a q-analog of some numbers and polynomials
(SPRINGER INTERNATIONAL PUBLISHING AG, 2015-01-20)
In this paper, we introduce new q-analogs of the Changhee numbers and polynomials of the first kind and of the second kind. We also derive some new interesting identities related to the Stirling numbers of the first kind ...
A General Class of the Three-Variable Unified Apostol-Type q-Polynomials and Multiple Power q-Sums
(Springer International Publishing, 2019)
The main purpose of this article is to introduce a general class of the three-variable unified Apostol-type q-polynomials and to investigate their properties and characteristics. In particular, the generating function, ...
Certain fractional calculus formulas involving extended generalized Mathieu series
(SPRINGEROPEN, 2018-04-23)
We establish fractional integral and derivative formulas by using fractional calculus operators involving the extended generalized Mathieu series. Next, we develop their composition formulas by applying the integral ...
A new approach to Legendre-truncated-exponential-based Sheffer sequences via Riordan arrays
(Elsevier Inc., 2020-03-15)
The significance of multi-variable special polynomials has been identified both in mathematical and applied frameworks. The article aims to focus on a new class of 3-variable Legendre-truncated-exponential-based Sheffer ...
A STUDY ON SOME NEW RESULTS ARISING FROM (p, q)-CALCULUS
(INST APPLIED MATHEMATICS, 2020)
This paper includes some new investigations and results for post quantum calculus, denoted by (p, q)-calculus. A chain rule for (p, q)-derivative is given. Also, a new (p, q)-analogue of the exponential function is introduced ...
Research on Some New Results Arising from Multiple q-Calculus
(UNIV NIS, 2018)
In this paper, we develop the theory of the multiple q-analogue of the Heine's binomial formula, chain rule and Leibniz's rule. We also derive many useful definitions and results involving multiple q-antiderivative and ...
A novel approach for obtaining new identities for the lambda extension of q- Euler polynomials arising from the q-umbral calculus
(INT SCIENTIFIC RESEARCH PUBLICATIONS, 2017)
In this article, a new q-generalization of the Apostol-Euler polynomials is introduced using the usual q-exponential function. We make use of such a generalization to derive several properties arising from the q-umbral ...
Construction of Fourier expansion of Apostol Frobenius-Euler polynomials and its applications
(SPRINGEROPEN, 2018-02-22)
In the present paper, we find the Fourier expansion of the Apostol Frobenius-Euler polynomials. By using a Fourier expansion of the Apostol Frobenius-Euler polynomials, we derive some new and interesting results.
On an Analogue of Euler Polynomials and Related to Extended Fermionic p-Adic Integrals on Z(p)
(SPRINGER INTERNATIONAL PUBLISHING AG, 2017-09)
In the paper, using the extended fermionic p-adic integral on Z(p), the authors find some applications of the umbral calculus. From these applications, the authors derive some identities on the weighted Euler numbers and ...
