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

Year 2017, Volume: 5 Issue: 1, 49 - 55, 01.04.2017

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 $S_4$.

References

  • [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.
Year 2017, Volume: 5 Issue: 1, 49 - 55, 01.04.2017

Abstract

References

  • [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.
There are 21 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

UGUR Duran

MEHMET Acıkgoz

Publication Date April 1, 2017
Submission Date February 14, 2017
Acceptance Date November 21, 2016
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA 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, 5(1), 49-55.
AMA Duran U, Acıkgoz M. NOVEL IDENTITIES INVOLVING GENERALIZED CARLITZ’S TWISTED $q$-EULER POLYNOMIALS ATTACHED TO $\chi$ UNDER $S_4$. Konuralp J. Math. April 2017;5(1):49-55.
Chicago Duran, UGUR, and MEHMET Acıkgoz. “NOVEL IDENTITIES INVOLVING GENERALIZED CARLITZ’S TWISTED $q$-EULER POLYNOMIALS ATTACHED TO $\chi$ UNDER $S_4$”. Konuralp Journal of Mathematics 5, no. 1 (April 2017): 49-55.
EndNote Duran U, Acıkgoz M (April 1, 2017) NOVEL IDENTITIES INVOLVING GENERALIZED CARLITZ’S TWISTED $q$-EULER POLYNOMIALS ATTACHED TO $\chi$ UNDER $S_4$. Konuralp Journal of Mathematics 5 1 49–55.
IEEE U. Duran and M. Acıkgoz, “NOVEL IDENTITIES INVOLVING GENERALIZED CARLITZ’S TWISTED $q$-EULER POLYNOMIALS ATTACHED TO $\chi$ UNDER $S_4$”, Konuralp J. Math., vol. 5, no. 1, pp. 49–55, 2017.
ISNAD Duran, UGUR - Acıkgoz, MEHMET. “NOVEL IDENTITIES INVOLVING GENERALIZED CARLITZ’S TWISTED $q$-EULER POLYNOMIALS ATTACHED TO $\chi$ UNDER $S_4$”. Konuralp Journal of Mathematics 5/1 (April 2017), 49-55.
JAMA Duran U, Acıkgoz M. NOVEL IDENTITIES INVOLVING GENERALIZED CARLITZ’S TWISTED $q$-EULER POLYNOMIALS ATTACHED TO $\chi$ UNDER $S_4$. Konuralp J. Math. 2017;5:49–55.
MLA Duran, UGUR and MEHMET Acıkgoz. “NOVEL IDENTITIES INVOLVING GENERALIZED CARLITZ’S TWISTED $q$-EULER POLYNOMIALS ATTACHED TO $\chi$ UNDER $S_4$”. Konuralp Journal of Mathematics, vol. 5, no. 1, 2017, pp. 49-55.
Vancouver Duran U, Acıkgoz M. NOVEL IDENTITIES INVOLVING GENERALIZED CARLITZ’S TWISTED $q$-EULER POLYNOMIALS ATTACHED TO $\chi$ UNDER $S_4$. Konuralp J. Math. 2017;5(1):49-55.
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