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ON THE SYMMETRIC IDENTITIES OF MODIFIED DEGENERATE BERNOULLI POLYNOMIALS

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Recently, Dolgy-Kim-Kwon-Seo introduced the modified de- generate Bernoulli polynomials which are different from Carlitz's degener- ate Bernoulli polynomials(see [5]). In this paper, we investigate some sym- metric identities for the modified degenerate Bernoulli polynomials arising from p-adic invariant integral on Zp.

Abstract

Recently, Dolgy-Kim-Kwon-Seo introduced the modified de- generate Bernoulli polynomials which are different from Carlitz's degener- ate Bernoulli polynomials(see [5]). In this paper, we investigate some sym- metric identities for the modified degenerate Bernoulli polynomials arising from p-adic invariant integral on Zp.

참고문헌 (20)

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  2. L. Carlitz, "Degenerate Stirling, Bernoulli and Eulerian numbers", Utilitas Math, 15, pp.51~88 (1979)
  3. L. Carlitz, "A degenerate Staudt- Clausen theorem", Arch. Math.(Basel), 7, pp.28~33 (1956)
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  6. D. V. Dolgy, "Symmetry identities for the generalized higher-order q-Bernoulli polynomials under arising from -adic Volkenborn ingegral on Z_p", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 17(4), pp.645~650 (2014), 장전수학회
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  8. 강동진, "ON THE TWISTED WEAK WEIGHT q-BERNOULLI POLYNOMIALS AND NUMBERS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 16(2), pp.195~201 (2013), 장전수학회
  9. 김대산, "Abundant symmetry for higher-order Bernoulli polynomials (II)", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 16(3), pp.359~378 (2013), 장전수학회
  10. 김대산, "Abundant symmetry for higher-order Bernoulli polynomials (I)", Advanced Studies in Contemporary Mathematics, 23(3), pp.459~479 (2013), 장전수학회
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  12. 김대산, "A note on Eulerian polynomials associated with Bernoulli and Euler numbers and polynomials", Advanced Studies in Contemporary Mathematics, 22(3), pp.379~389 (2012), 장전수학회[DOI]
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  17. J. W. Park, "On the modified -Bernoulli polynomials with weight", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 17(2), pp.231~236 (2014), 장전수학회
  18. 박진우, "New approach to -Bernoulli polynomials with weight or weak weight", Advanced Studies in Contemporary Mathematics, 24(1), pp.39~44 (2014), 장전수학회
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  20. Z. Zhang, "Some closed formulas for generalizations of Bernoulli and Euler numbers and polynomials", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 11(2), pp.191~198 (2008), 장전수학회

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