Some results on power sums and Apostol-type polynomials

Abstract

In this paper, we study the Apostol–Bernoulli polynomials, the Apostol–Euler polynomials and the power sums with respect to λ. As a result, various identities are established, including the multiplication formulae of the Apostol-type polynomials, some symmetric identities and some convolution identities.

Keywords:

• Apostol–Bernoulli polynomials
• Apostol–Euler polynomials
• power sums
• multiplication formulae
• combinatorial identities

Acknowledgements

The authors would like to thank the referee for his (her) careful reading and valuable comments. The first author is supported by the Postdoctoral Science Foundation of China under Grant 20080441037.