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q-Bernoulli polynomials and q-umbral calculus

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Abstract

In this paper, we investigate some properties of q-Bernoulli polynomials arising from q-umbral calculus. We find a formula for expressing any polynomial as a linear combination of q-Bernoulli polynomials with explicit coefficients. Also, we establish some connections between q-Bernoulli polynomials and higher-order q-Bernoulli polynomials.

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Authors and Affiliations

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

    Dae San Kim

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

    Tae Kyun Kim

Authors
  1. Dae San Kim
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  2. Tae Kyun Kim
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Correspondence to Tae Kyun Kim.

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Kim, D.S., Kim, T.K. q-Bernoulli polynomials and q-umbral calculus. Sci. China Math. 57, 1867–1874 (2014). https://doi.org/10.1007/s11425-014-4821-3

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  • DOI: https://doi.org/10.1007/s11425-014-4821-3

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