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)
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 numbersKeywords:
Apostol-Bernoulli polynomials and numbers; Apostol-Euler polynomials and numbers; Sheffer sequences; Appell sequences; Fibonacci numbers; umbral algebra; p-adic integral
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Simsek, Y. Special Numbers and Polynomials Including Their Generating Functions in Umbral Analysis Methods. Axioms 2018, 7, 22.
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