Modification and unification of the Apostol-type numbers and polynomials and their applications

Ozden, Hacer; ŞİMŞEK, YILMAZ

doi:10.1016/j.amc.2014.03.004

Modification and unification of the Apostol-type numbers and polynomials and their applications

Ozden H., ŞİMŞEK Y.

APPLIED MATHEMATICS AND COMPUTATION, vol.235, pp.338-351, 2014 (SCI-Expanded, Scopus)

Publication Type: Article / Article
Volume: 235
Publication Date: 2014
Doi Number: 10.1016/j.amc.2014.03.004
Journal Name: APPLIED MATHEMATICS AND COMPUTATION
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.338-351
Keywords: Bernoulli numbers and polynomials, Euler numbers and polynomials, Genocchi Bernoulli numbers and polynomials, Stirling numbers, Catalan numbers, UNIFIED PRESENTATION, EULER POLYNOMIALS, GENERATING-FUNCTIONS, BERNOULLI, FAMILIES, (H
Akdeniz University Affiliated: Yes

Abstract

In this paper, we construct generating functions for modification and unification of the Apostol-type polynomials Y ((nu))(n,beta)(x;k,a,b) of order nu. By using these generating functions, we derive many new identities related to the generalized Stirling type numbers of the second kind, array-type polynomials, Eulerian polynomials and the modification and unification of the Apostol-type polynomials and numbers. We give many applications related to these numbers and polynomials and PDEs. (C) 2014 Elsevier Inc. All rights reserved.