Next Article in Journal
Interval Neutrosophic Sets with Applications in BCK/BCI-Algebra
Next Article in Special Issue
New Definitions about A I -Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences
Previous Article in Journal
Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision-Making
Article Menu

Export Article

Open AccessArticle
Axioms 2018, 7(2), 22; https://doi.org/10.3390/axioms7020022

Special Numbers and Polynomials Including Their Generating Functions in Umbral Analysis Methods

Department of Mathematics, Faculty of Science University of Akdeniz, TR-07070 Antalya, Turkey
Received: 20 January 2018 / Revised: 27 March 2018 / Accepted: 30 March 2018 / Published: 1 April 2018
(This article belongs to the Special Issue Mathematical Analysis and Applications)
View Full-Text   |   Download PDF [800 KB, uploaded 3 May 2018]

Abstract

In this paper, by applying umbral calculus methods to generating functions for the combinatorial numbers and the Apostol type polynomials and numbers of order k, we derive some identities and relations including the combinatorial numbers, the Apostol-Bernoulli polynomials and numbers of order k and the Apostol-Euler polynomials and numbers of order k. Moreover, by using p-adic integral technique, we also derive some combinatorial sums including the Bernoulli numbers, the Euler numbers, the Apostol-Euler numbers and the numbers y 1 n , k ; λ . Finally, we make some remarks and observations regarding these identities and relations. View Full-Text
Keywords: Apostol-Bernoulli polynomials and numbers; Apostol-Euler polynomials and numbers; Sheffer sequences; Appell sequences; Fibonacci numbers; umbral algebra; p-adic integral Apostol-Bernoulli polynomials and numbers; Apostol-Euler polynomials and numbers; Sheffer sequences; Appell sequences; Fibonacci numbers; umbral algebra; p-adic integral
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Simsek, Y. Special Numbers and Polynomials Including Their Generating Functions in Umbral Analysis Methods. Axioms 2018, 7, 22.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top