Science China Mathematics

, Volume 62, Issue 5, pp 999–1028 | Cite as

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

  • Taekyun KimEmail author
  • Dae San Kim


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.


generalized Pascal functional matrix Wronskian matrix degenerate Bernoulli polynomial Krobov polynomial of the first kind 


05A19 05A40 11B83 


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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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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsKwangwoon UniversitySeoulRepublic of Korea
  2. 2.Department of MathematicsSogang UniversitySeoulRepublic of Korea

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