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Summation formulae of products of the Apostol–Bernoulli and Apostol–Euler polynomials

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Abstract

In this paper, a further investigation for the Apostol–Bernoulli and Apostol–Euler polynomials is performed, and some summation formulae of products of the Apostol–Bernoulli and Apostol–Euler polynomials are established by applying some summation transform techniques. Some illustrative special cases as well as immediate consequences of the main results are also considered.

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Acknowledgements

The author expresses his sincere gratitude to the anonymous referees for their helpful comments and suggestions, which have led to a significant improvement on the presentation of this paper.

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Authors and Affiliations

  1. Faculty of Science, Kunming University of Science and Technology, Kunming, 650500, Yunnan, People’s Republic of China

    Yuan He

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  1. Yuan He
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Correspondence to Yuan He.

Additional information

This work was supported by the Foundation for Fostering Talents in Kunming University of Science and Technology (Grant No.  KKSY201307047) and the National Natural Science Foundation of China (Grant No.  11326050).

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He, Y. Summation formulae of products of the Apostol–Bernoulli and Apostol–Euler polynomials. Ramanujan J 43, 447–464 (2017). https://doi.org/10.1007/s11139-017-9899-0

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  • DOI: https://doi.org/10.1007/s11139-017-9899-0

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