Journals / Konuralp Journal of Mathematics / 2026 / Volume: 5 Issue: 1

NOVEL IDENTITIES INVOLVING GENERALIZED CARLITZ'S TWISTED $q$-EULER POLYNOMIALS ATTACHED TO $\chi$ UNDER $S_4$

UGUR Duran(University of Gaziantep, Faculty of Science and Arts, Department of Mathematics, Gaziantep)
MEHMET Acıkgoz(University of Gaziantep, Faculty of Science and Arts, Department of Mathematics, Gaziantep)
Pages
—
Publication Date
2017-04-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The essential purpose of this paper is to give some novel symmetric identities for generalized Carlitz's twisted $q$-Euler polynomials attached to $\chi$ based on the fermionic $p$-adic invariant integral on $Z_p$ under $S_4$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The essential purpose of this paper is to give some novel symmetric identities for generalized Carlitz's twisted $q$-Euler polynomials attached to $\chi$ based on the fermionic $p$-adic invariant integral on $Z_p$ under $S_4$.
📊
Key Findings & Data:The essential purpose of this paper is to give some novel symmetric identities for generalized Carlitz's twisted $q$-Euler polynomials attached to $\chi$ based on the fermionic $p$-adic invariant integral on $Z_p$ under $S_4$.
💡
Conclusion & Impact:The essential purpose of this paper is to give some novel symmetric identities for generalized Carlitz's twisted $q$-Euler polynomials attached to $\chi$ based on the fermionic $p$-adic invariant integral on $Z_p$ under $S_4$.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Fermionic p-adic invariant integral on Zp · Invariant under S4 · Sym- metric identities

Abstract

The essential purpose of this paper is to give some novel symmetric identities for generalized Carlitz's twisted $q$-Euler polynomials attached to $\chi$ based on the fermionic $p$-adic invariant integral on $Z_p$ under $S_4$.

🔖

Cite This Article

Duran, U., Acıkgoz, M. (2017). NOVEL IDENTITIES INVOLVING GENERALIZED CARLITZ'S TWISTED $q$-EULER POLYNOMIALS ATTACHED TO $\chi$ UNDER $S_4$. Konuralp Journal of Mathematics, Volume: 5 Issue: 1. https://ajindex.com/articles/1521862

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (21)

  1. Apostol T. M., Introduction to Analytic Number Theory, New York, Splinger-Verlag, 1976.
  2. Araci S., Acikgoz M., Bagdasaryan A., Sen E., The Legendre polynomials associated with Bernoulli, Euler, Hermite and Bernstein polynomials, Turkish J. Anal. Number Theory, 1(2013), no. 1, 1-3.
  3. Araci S., Duran U., Acikgoz M., Symmetric identities involving q-Frobenius-Euler polynomials under Sym (5), Turkish J. Anal. Number Theory, 3(2015), no. 3, 90-93.
  4. Choi J., Anderson P. J., and Srivastava H. M., \Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler Polynomials of Order n and the Multiple Hurwitz Zeta Function," Appl. Math. Comput., 199(2008), 723{737.
  5. Choi J., Anderson P. J., and Srivastava H. M., \Carlitz's q-Bernoulli and q-Euler Numbers and Polynomials and a Class of q-Hurwitz Zeta Functions," Appl. Math. Comput., 215(2009), 1185-1208.
  6. Dolgy D. V., Jang Y. S., Kim T., Kwon H. I., Seo J.-J., Identities of symmetry for q-Euler polynomials derived from fermionic integral on Zp under symmetry group S3, Appl. Math. Sci., 8(2014), no. 113, 5599-5607.
  7. Dolgy D. V., Kim T., Rim S.-H., Lee S.-H, Some Symmetric Identities for h-Extension of q-Euler Polynomials
  8. Duran U., Acikgoz M., Esi A., Araci S., Some new symmetric identities involving q-Genocchi polynomials under S4, J. Math. Anal., 6(2015), no. 4, 22-31.
  9. Duran U., Acikgoz M., Araci S., Symmetric identities involving weighted q-Genocchi polyno mials under S4, Proc. Jangjeon Math. Soc., 18(2015), No. 4, 455-465.
  10. Duran U., Acikgoz M., New identities for Carlitz's twisted (h; q)-Euler polynomials under symmetric group of degree n, J. Anal. Number Theory, (2016), 4(2016), no. 2 133-137.
  11. Kim T., On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Zp at q = 1, J. Math. Anal. Appl., 331(2007), 779-792.
  12. Kim T., Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on Zp, Russ. J. Math. Phys., 16(2009), no. 4, 484-491.
  13. Kim T., A note on the p-adic invariant integral in the rings of p-adic integers, arXiv:math/0606097v1 [math.NT] (2006).
  14. Ozden H., Simsek Y., and Cangul I. N., Euler polynomials associated with p-adic q-Euler measure, Gen. Math., 15(2007), No. 2-3, 24-37.
  15. Rim S. H., Kim T., Lee S. H., Symmetric identities of generalized (h; q)-Euler polynomials under third dihedral group, Appl. Math. Sci., 8(2014), no. 145, 7207-7212.
  16. Ryoo C. S., Symmetric properties for Carlitz's twisted (h; q)-Euler polynomials associated with p-adic q-integral on Zp, Internat. J. Math. Anal., Vol. 9 (2015), no. 40, 1947 - 1953.
  17. Ryoo C. S., Symmetric properties for Carlitz's twisted q-Euler numbers and polynomials associated with p-adic integral on Zp, Internat. J. Math. Anal., 9 (2015), no. 83, 4129 - 4134.
  18. Seo J. J., Kim T., Identities of symmetry for generalized q{Euler polynomials attached to ksi under symmetric group S4, Adv. Stud. Theoret. Phys., 9(2015), no. 8, 353-359.
  19. Simsek Y., Complete sum of products of (h; q)-extension of Euler polynomials and numbers, J. Difference Equ. Appl., 16(2010), no. 11, 1331-1348.
  20. Srivastava H. M., Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inf. Sci., 5(2011), 390-444.
  21. Srivastava H. M., Kim T., and Simsek Y., q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, Russ. J. Math Phys., 12(2005), 241{268.