Bulletin of the Korean Mathematical Society (대한수학회보)

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UNIFIED APOSTOL-KOROBOV TYPE POLYNOMIALS AND RELATED POLYNOMIALS

  • Kurt, Burak (Mathematics of Department Education of Faculty Akdeniz University)
  • Received : 2020.03.16
  • Accepted : 2020.07.09
  • Published : 2021.03.31
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Abstract

Korobov type polynomials are introduced and extensively investigated many mathematicians ([1, 8-10, 12-14]). In this work, we define unified Apostol Korobov type polynomials and give some recurrences relations for these polynomials. Further, we consider the q-poly Korobov polynomials and the q-poly-Korobov type Changhee polynomials. We give some explicit relations and identities above mentioned functions.

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References

  1. M. Ali Ozarslan, Unified Apostol-Bernoulli, Euler and Genocchi polynomials, Comput. Math. Appl. 62 (2011), no. 6, 2452-2462. https://doi.org/10.1016/j.camwa.2011.07.031
  2. A. Bayad and Y. Hamahata, Polylogarithms and poly-Bernoulli polynomials, Kyushu J. Math. 65 (2011), no. 1, 15-24. https://doi.org/10.2206/kyushujm.65.15
  3. L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math. 15 (1979), 51-88.
  4. L. Carlitz, Weighted Stirling numbers of the first and second kind. I, Fibonacci Quart. 18 (1980), no. 2, 147-162.
  5. Y. Hamahata, Poly-Euler polynomials and Arakawa-Kaneko type zeta functions, Funct. Approx. Comment. Math. 51 (2014), no. 1, 7-22. https://doi.org/10.7169/facm/2014.51.1.1
  6. K. W. Hwang, B. R. Nam, and N. S. Jung, A note on q-analogue of poly-Bernoulli numbers and polynomials, J. Appl. Math. Inform. 35 (2017), no. 5-6, 611-621. https://doi.org/10.14317/jami.2017.611
  7. K. Imatomi, M. Kaneko, and E. Takeda, Multi-poly-Bernoulli numbers and finite multiple zeta values, J. Integer Seq. 17 (2014), no. 4, Article 14.4.5, 12 pp.
  8. D. S. Kim and T. Kim, A note on poly-Bernoulli and higher-order poly-Bernoulli polynomials, Russ. J. Math. Phys. 22 (2015), no. 1, 26-33. https://doi.org/10.1134/S1061920815010057
  9. D. S. Kim and T. Kim, Some identities of Korobov-type polynomials associated with p-adic integrals on ℤp, Adv. Difference Equ. 2015 (2015), 282, 13 pp. https://doi.org/10.1186/s13662-015-0602-8
  10. D. S. Kim, T. Kim, H. I. Kwon, and T. Mansour, Korobov polynomials of the fifth kind and of the sixth kind, Kyungpook Math. J. 56 (2016), no. 2, 329-342. https://doi.org/10.5666/KMJ.2016.56.2.329
  11. T. Kim, Multiple zeta values, Di-zeta values and their applications, Lecture notes in number theory Graduate schools, Kyungnom Univ., 1998.
  12. T. Kim and D. S. Kim, Korobov polynomials of the third kind and of the fourth kind, Springer plus, 4 (2015), 608.
  13. T. Komatsu, J. L. Ramirez, and V. F. Sirvent, A (p, q)-analogue of poly-Euler polynomials and some related polynomials, arxiv:1604.2016.
  14. D. V. Kruchinin, Explicit formulas for Korobov polynomials, Proc. Jangjeon Math. Soc. 20 (2017), no. 1, 43-50.
  15. J. J. Seo and T. Kim, Degenerate Korobov polynomials, App. Math. Sci. 10 (2016), no. 4, 167-173. https://doi.org/10.1007/s40096-016-0191-z
  16. H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inf. Sci. 5 (2011), no. 3, 390-444.
  17. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, 2001.
  18. H. M. Srivastava, M. Garg, and S. Choudhary, A new generalization of the Bernoulli and related polynomials, Russ. J. Math. Phys. 17 (2010), no. 2, 251-261. https://doi.org/10.1134/S1061920810020093