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Identities for degenerate Bernoulli polynomials and Korobov polynomials of the first kind

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Abstract

In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply twelve basic identities for Sheffer polynomials, seven from previous results, to degenerate Bernoulli polynomials and Korobov polynomials of the first kind and get some new identities. In addition, letting λ → 0 in such identities gives us those for Bernoulli polynomials and Bernoulli polynomials of the second kind.

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Acknowledgements

This work was supported by the Research Grant of Kwangwoon University in 2018. The authors thank the referees for their valuable suggestions which improved the original manuscript greatly.

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Authors and Affiliations

  1. Department of Mathematics, Kwangwoon University, Seoul, 139-701, Republic of Korea

    Taekyun Kim

  2. Department of Mathematics, Sogang University, Seoul, 121-742, Republic of Korea

    Dae San Kim

Authors
  1. Taekyun Kim
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  2. Dae San Kim
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Correspondence to Taekyun Kim.

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Kim, T., Kim, D.S. Identities for degenerate Bernoulli polynomials and Korobov polynomials of the first kind. Sci. China Math. 62, 999–1028 (2019). https://doi.org/10.1007/s11425-018-9338-5

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  • DOI: https://doi.org/10.1007/s11425-018-9338-5

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