Open Access Research

Some properties of the generalized Apostol-type polynomials

Da-Qian Lu1 and Qiu-Ming Luo2*

Author Affiliations

1 Department of Mathematics, Yangzhou University, Yangzhou, Jiangsu, 225002, People’s Republic of China

2 Department of Mathematics, Chongqing Normal University, Chongqing Higher Education Mega Center, Huxi Campus, Chongqing, 401331, People’s Republic of China

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Boundary Value Problems 2013, 2013:64  doi:10.1186/1687-2770-2013-64

Published: 28 March 2013

Abstract

In this paper, we study some properties of the generalized Apostol-type polynomials (see (Luo and Srivastava in Appl. Math. Comput. 217:5702-5728, 2011)), including the recurrence relations, the differential equations and some other connected problems, which extend some known results. We also deduce some properties of the generalized Apostol-Euler polynomials, the generalized Apostol-Bernoulli polynomials, and Apostol-Genocchi polynomials of high order.

MSC: 11B68, 33C65.

Keywords:
generalized Apostol type polynomials; recurrence relations; differential equations; connected problems; quasi-monomial