Some unified formulas and representations for the Apostol-type polynomials

Advances in Difference Equations

Da-Qian Lu¹  Qiu-Ming Luo³ 

[1] Department of Mathematics and Information, Taizhou University, Taizhou, People’Department of Mathematics, Chongqing Normal University, Chongqing, People’s Republic of China

关键词: (generalized) Apostol-type polynomials;    Apostol-Euler polynomials;    Apostol-Bernoulli polynomials;    Genocchi polynomials of high order;    multiplication formula;    Gaussian hypergeometric function;    (generalized) Hurwitz zeta function;    11B68;    11M35;    11B73;    33C05;   

DOI  :  10.1186/s13662-015-0480-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Recently, a family of the Apostol-type polynomials was introduced by Luo and Srivastava (Appl. Math. Comput. 217:5702-5728 (2011)). In this paper, we further investigate the Apostol-type polynomials and obtain their unified multiplication formula and explicit representations in terms of the Gaussian hypergeometric function and the generalized Hurwitz zeta function. We also show some special cases, which include the corresponding results of Luo, Garg, Srivastava, Ozden, and Özarslan etc.

【 授权许可】

CC BY