Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials
Hanrimwon, Kwangwoon University, Seoul 139-701, Korea
Department of Mathematics, Sogang University, Seoul 121-742, Korea
Department of Mathematics Education and ERI, Gyeongsang National University, Jinju, Gyeongsangnamdo 52828, Korea
Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea
Author to whom correspondence should be addressed.
Received: 28 May 2019 / Revised: 25 June 2019 / Accepted: 26 June 2019 / Published: 1 July 2019
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In this paper, we investigate some identities on Bernoulli numbers and polynomials and those on degenerate Bernoulli numbers and polynomials arising from certain p
-adic invariant integrals on
. In particular, we derive various expressions for the polynomials associated with integer power sums, called integer power sum polynomials and also for their degenerate versions. Further, we compute the expectations of an infinite family of random variables which involve the degenerate Stirling polynomials of the second and some value of higher-order Bernoulli polynomials.
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MDPI and ACS Style
Dolgy, D.V.; Kim, D.S.; Kwon, J.; Kim, T. Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials. Symmetry 2019, 11, 847.
Dolgy DV, Kim DS, Kwon J, Kim T. Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials. Symmetry. 2019; 11(7):847.
Dolgy, Dmitry V.; Kim, Dae S.; Kwon, Jongkyum; Kim, Taekyun. 2019. "Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials." Symmetry 11, no. 7: 847.
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