Unified Apostol-Bernoulli, Euler and Genocchi polynomials

作者：Ozarslan M Ali^*

来源：Computers & Mathematics with Applications, 2011, 62(6): 2452-2462.

DOI：10.1016/j.camwa.2011.07.031

• Apostol-Bernoulli polynomials
• Apostol-Euler polynomials
• Apostol-Genocchi polynomials
• Gaussian hypergeometric function
• Pfaff-Kummer transformation
• Generalized multinomial identity

In this paper, we present a unified family of polynomials including not only the Apostol-Bernoulli, Euler and Genocchi polynomials, but also a general family of polynomials suggested by Ozden et al. [H. Ozden, Y. Simsek, H.M. Srivastava, A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials. Comput. Math. Appl. 60 (10) (2010) 2779-2787]. We obtain the explicit representation of this unified family, in terms of a Gaussian hypergeometric function. Some symmetry identities and multiplication formula are also given.

• 出版日期2011-9