• Title, Summary, Keyword: q-Bernoulli polynomial

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SOME REMARKS ON A q-ANALOGUE OF BERNOULLI NUMBERS

  • Kim, Min-Soo;Son, Jin-Woo
    • Journal of the Korean Mathematical Society
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    • v.39 no.2
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    • pp.221-236
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    • 2002
  • Using the p-adic q-integral due to T. Kim[4], we define a number B*$_{n}$(q) and a polynomial B*$_{n}$(q) which are p-adic q-analogue of the ordinary Bernoulli number and Bernoulli polynomial, respectively. We investigate some properties of these. Also, we give slightly different construction of Tsumura's p-adic function $\ell$$_{p}$(u, s, $\chi$) [14] using the p-adic q-integral in [4].n [4].

MORE EXPANSION FORMULAS FOR q, ��-APOSTOL BERNOULLI AND EULER POLYNOMIALS

  • Ernst, Thomas
    • Communications of the Korean Mathematical Society
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    • v.35 no.2
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    • pp.417-445
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    • 2020
  • The purpose of this article is to continue the study of q, ��-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, ��-Apostol Bernoulli and Euler polynomials, Ward-�� numbers and multiple q, ��power sums. Like before, the q, ��-module for the alphabet of q, ��-real numbers plays a crucial role, as well as the q, ��-rational numbers and the Ward-�� numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.

SOME RELATIONSHIPS BETWEEN (p, q)-EULER POLYNOMIAL OF THE SECOND KIND AND (p, q)-OTHERS POLYNOMIALS

  • KANG, JUNG YOOG;AGARWAL, R.P.
    • Journal of applied mathematics & informatics
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    • v.37 no.3_4
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    • pp.219-234
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    • 2019
  • We use the definition of Euler polynomials of the second kind with (p, q)-numbers to identify some identities and properties of these polynomials. We also investigate some relationships between (p, q)-Euler polynomials of the second kind, (p, q)-Bernoulli polynomials, and (p, q)-tangent polynomials by using the properties of (p, q)-exponential function.