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On the integral of the product of four and more Bernoulli polynomials

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Abstract

In 1958, L.J. Mordell provided a formula for the integral of the product of two Bernoulli polynomials. He also remarked: “The integrals containing the product of more than two Bernoulli polynomials do not appear to lead to simple results.” In this paper, we provide explicit formulas for the integral of the product of r Bernoulli polynomials, where r is any positive integer. Many results in this direction, including those by Nörlund, Mordell, Carlitz, Agoh, and Dilcher, are special cases of the formulas given in this paper.

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Acknowledgements

The authors are grateful to the anonymous referee for his/her helpful comments.

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Author notes

  1. Su Hu

    Present address: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montréal, Québec, H3A 2K6, Canada

Authors and Affiliations

  1. Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 305-701, South Korea

    Su Hu

  2. National Institute for Mathematical Sciences, Doryong-dong, Yuseong-gu, Daejeon, 305-340, South Korea

    Daeyeoul Kim

  3. Division of Cultural Education, Kyungnam University, 7(Woryeongdong) kyungnamdaehak-ro, Masanhappo-gu, Changwon-si, Gyeongsangnam-do, 631-701, South Korea

    Min-Soo Kim

Authors
  1. Su Hu
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  2. Daeyeoul Kim
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  3. Min-Soo Kim
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Corresponding author

Correspondence to Min-Soo Kim.

Additional information

This work was supported by the Kyungnam University Foundation Grant, 2013.

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Hu, S., Kim, D. & Kim, MS. On the integral of the product of four and more Bernoulli polynomials. Ramanujan J 33, 281–293 (2014). https://doi.org/10.1007/s11139-013-9506-y

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  • DOI: https://doi.org/10.1007/s11139-013-9506-y

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