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A NOTE ON TYPE 2 DEGENERATE POLY-GENOCCHI POLYNOMIALS AND NUMBERS OF COMPLEX VARIABLE ARISING FROM THE DEGENERATE MODIFIED POLYEXPONENTIAL FUNCTION

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초록

In recent years, the study of degenerate versions of some special polynomials and num- bers regained interests of many mathematicians. Kim et al.(Adv. Differ. Equ., 2019:490, 2019) studied the type 2 degenerate Bernoulli and Euler polynomials of complex variable. In this paper, we introduce the type 2 degenerate poly-Genocchi polynomials and numbers of complex variable, based on Kim and Kim’s modified polyexponential function(Russ. J. Math. Phys. 26(1), 2019). We derive several identities related to the type 2 degenerate poly-cosine(sine)-Genocchi polynomials and numbers, including the degenerate and other special polynomials and numbers such as the (degener- ate) Stirling numbers of the first kind, the (degenerate) Stirling numbers of the second kind, type 2 cosine-Genocchi polynomials, type 2 sine-Genocchi polynomials, etc.

Abstract

In recent years, the study of degenerate versions of some special polynomials and num- bers regained interests of many mathematicians. Kim et al.(Adv. Differ. Equ., 2019:490, 2019) studied the type 2 degenerate Bernoulli and Euler polynomials of complex variable. In this paper, we introduce the type 2 degenerate poly-Genocchi polynomials and numbers of complex variable, based on Kim and Kim’s modified polyexponential function(Russ. J. Math. Phys. 26(1), 2019). We derive several identities related to the type 2 degenerate poly-cosine(sine)-Genocchi polynomials and numbers, including the degenerate and other special polynomials and numbers such as the (degener- ate) Stirling numbers of the first kind, the (degenerate) Stirling numbers of the second kind, type 2 cosine-Genocchi polynomials, type 2 sine-Genocchi polynomials, etc.

참고문헌 (28)

  1. I. N.. Cangul, "ON THE HIGHER-ORDER w-q-GENOCCHI NUMBERS", Advanced Studies in Contemporary Mathematics, 19(1), pp.39~57 (2009), 장전수학회
  2. Carlitz, L, "Degenerate Stirling, Bernoulli and Eulerian numbers", Utilitas Math, 15, pp.51~88 (1979)
  3. NESLIHAN KILAR, "Relations on Bernoulli and Euler polynomials related to trigonometric functions", Advanced Studies in Contemporary Mathematics, 29(2), pp.191~198 (2019), 장전수학회
  4. Kilar, N, "Two parametric kinds of Eulerian-type polynomials associated with Euler’s formula", Symmetry, 11, pp.1~19 (2019)
  5. Kilar, N, "Some classes of generating functions for generalized Hermite and Chebyshev-type polynomials:Analysis of Euler’s formula", 1~31 (2019)
  6. Kilar, N, "A note on Hermite-based Milne Thomson type polynomials involving Chebyshev polynomials and other polynomials", Techno-Science, 3(1), pp.8~14 (2020)
  7. Kim, D. S, "A note on degenerate Euler and Bernoulli polynomials of complex variable", Symmetry, 11, pp.1168~ (2019)
  8. Kim, D. S, "A note on polyexponential and unipoly functions", Russ. J. Math. Phys, 26(1), pp.40~49 (2019)
  9. 김대산, "SOME IDENTITIES FOR BERNOULLI NUMBERS OF THE SECOND KIND ARISING FROM A NON-LINEAR DIFFERENTIAL EQUATION", 대한수학회보, 52(6), pp.2001~2010 (2015), 대한수학회
  10. Kim, D.S, "A note on a new type of degenerate Bernoulli numbers", Russ. J. Math. Phys, 27(2), pp.227~235 (2020)
  11. Kim, D. S, "On type 2 degenerate Bernoulli and Euler polynomials of complex variable", Adv. Differ. Equ, 2019, pp.490~ (2019)
  12. Kim, H. K, "A note on degenerate poly-Genocchi numbers and polynomials", Adv. Differ. Equ, 2020, pp.392~ (2020)
  13. 김택연, "A note on degenerate stirling polynomials of the second kind", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(3), pp.319~332 (2017), 장전수학회[DOI]
  14. Kim, T, "Some identities of type 2 degenerate Bernoulli polynomials of the second kind", Symmetry, 2020 (2020)
  15. Kim, T, "Degenerate polyexponential functions and degenerate Bell polynomials", J. Math. Anal. appl, 487(2), pp.124017~ (2020)
  16. Kim, T, "Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials", Adv. Difference Equ, 168, pp.12~ (2020)
  17. Kim, T, "A note on central Bell numbers and polynomials", Russ. J. Math. Phys, 27(1), pp.76~81 (2020)
  18. Kim, T, "Identities of symmetry for degenerate Euler polynomials and alternating generalized falling factorial sums", Iran. J. Sci. Technol. Trans. A Sci, 41(4), pp.939~949 (2017)
  19. Kim, T, "Degenerate Stirling polynomials of the second kind and some applications", Symmetry, 11(8), pp.11~ (2019)
  20. Kim, T, "Some identities for Euler and Bernoulli polynomials and their zeros", Axioms, 7(3), pp.1~19 (2018)
  21. BURAK KURT, "On the Hermite based Genocchi polynomials", Advanced Studies in Contemporary Mathematics, 23(1), pp.13~17 (2013), 장전수학회
  22. Liu, C, "Application of probabilistic method on Daehee sequences", Eur. J. Pure Appl. Math, 11(1), pp.69~78 (2018)
  23. Masjed-Jamei, M, "A new type of Euler polynomials and numbers", Mediterr. J. Math, 15, pp.138~ (2018)
  24. Masjed-Jamei, M, "An extension of the Euler-Maclauin quadrature formula using a parametric type of Bernoulli polynomials", ~ (2019)
  25. Pak. H.-k, "Changhee-Genocchi numbers and their applications", Ars Combin, 136, pp.153~159 (2018)
  26. Roman, S, "The umbral calculus, Pure and Applied Mathematics 111" (1984), Academic Press, Inc
  27. Simsek, Y, "q-Genocchi numbers and polynomials associated with q-Genocchi type functions", Adv. Difference Equ, 2008, pp.12~ (2008)
  28. Wuyungaowa, "Identities on products of Genocchi numbers", J. Inequal. Appl, 422, pp.10~ (2013)

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