A NOTE ON q-ANALOGUE OF POLY-GENOCCHI
NUMBERS AND POLYNOMIALS

Abstract

In this paper, we introduce a q-analogue of the poly-Genocchi numbers and polynomials which is a generalization of the poly-Genocchi numbers and polynomials including q-polylogarithm function. We also give the relation between generalized poly-Genocchi polynomials. We derive some relations that are connected with the Stirling numbers of the second kind. By using special functions, we investigate some symmetric identities involving q-poly-Genocchi polynomials.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 1
Year: 2022

DOI: 10.12732/ijam.v35i1.7

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References

  1. [1] L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J., 15 (1948), 9871000.
  2. [2] M. Cenkci, M. Can, and V. Kurt, q-extensions of Genocchi numbers, J. Korean Math. Soc., 43, No 1 (2006), 183-198.
  3. [3] N.S. Jung, C.S. Ryoo, Symmetric identities for degenerate q-poly-Bernoulli numbers and polynomials, J. Appl. Math. and Inform., 36, No 1-2 (2018), 29-38.
  4. [4] M. Kaneko, Poly-Bernoulli numbers, J. de Theorie de Nombres 9 (1997), 221-228.
  5. [5] W.A. Khan, H. Haroon, Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials, Springer Plus, 5 (2016), 1920; DOI 10.1186/s40064-016-3585-3.
  6. [6] W.A. Khan, S. Araci, M. Acikgoz, H. Haroon, A new class of partially degenerate Hermite-Genocchi polynomials, J. Nonlinear Sci. Appl., 10 (2017), 5072-5081.
  7. [7] W.A. Khan, I.A. Khan, M. Ali, A note on q-analogue of Hermite-polyBernoulli numbers and polynomials, Mathematica Morvica, 23, No 2 (2019), 1-16.
  8. [8] W.A. Khan and M. Ahmad, Partially degenerate poly-Bernoulli polynomials associated with Hermite polynomials, Adv. Stud. Contemp. Math. (Kyungshang) 28, No 3 (2018), 487-496.
  9. [9] W.A. Khan, A new class of degenerate Frobenius-Euler-Hermite polynomials, Adv. Stud. Contemp. Math. (Kyungshang) 28, No 4 (2018), 567-576. 102 M. Nadeem, W.A. Khan, M. Shadab
  10. [10] W.A. Khan, M. Acikgoz, U. Duran, Note on the type 2 degenerate multipoly-Euler polynomials, Symmetry, 12 (2020), 1-10.
  11. [11] W.A. Khan, R. Ali, K.A.H. Alzobydi, N. Ahmed, A new family of degenerate poly-Genocchi polynomials with its certain properties, J. Function Spaces, 2021 (2021), Art. ID 6660517, 8 pp.
  12. [12] T. Kim, q-generalized Euler numbers and polynomials, Russ. J. Math. Phys., 13, No 3 (2006), 293-298.
  13. [13] T. Kim, On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl., 326, No 2 (2007), 1458-1465.
  14. [14] T. Kim, A note on the q-Genocchi numbers and polynomials, J. Inequal. Appl., 2007 (2007), Art. ID 71452, 8 pp.; doi:10.1155/2007/71452.
  15. [15] T. Kim, Note on q-Genocchi numbers and polynomials,Adv. Stud. Contemp. Math., (Kyungshang) 17, No 1 (2008), 9-15.
  16. [16] T. Kim, Y. S. Jang and J. J. Seo, A note on poly-Genocchi numbers and polynomials, Appl. Math. Sci., 8 (2014), 4475-4781.
  17. [17] Y. Simsek, I.N. Cangul, V. Kurt, and D. Kim, q-Genocchi numbers and polynomials associated with q-Genocchi-type l-functions, Adv. Difference Equ., 2008 (2008), Art. ID 815750, 12 pp.; doi:10.11555.2008/85750.
  18. [18] H.M. Srivastava and A. Pinter, Remarks on some relationships between the Bernoulli and Euler polynomials, Appl. Math. Lett., 17, No 4 (2004), 375-380.
  19. [19] S.K. Sharma, A note on degenerate poly-Genocchi polynomials. Int. J. Adv. Appl. Sci., 7, No 5(2020), 1-5.