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BibTex RIS Kaynak Göster

Yıl 2016, Cilt: 4 Sayı: 2, 52 - 57, 30.10.2016

Ugur Duran , Mehmet Acikgoz

https://doi.org/10.36753/mathenot.421455

Öz

Kaynakça

  • [1] T. M. Apostol, Introduction to Analytic Number Theory, New York; Splinger-Verlag, (1976).
  • [2] M. Acikgoz, S. Araci, U.Duran, New extensions of some known special polynomials under the theory of multiple q-calculus, Turkish Journal of Analysis and Number Theory, Vol. 3, No. 5, (2015) pages 128-139.
  • [3] S. Araci, U. Duran, M. Acikgoz, Symmetric identities involving q-Frobenius-Euler polynomials under Sym (5), Turkish Journal of Analysis and Number Theory, Vol. 3, No. 3, pp. 90-93 (2015).
  • [4] J. Choi, P. J. Anderson, H. M. Srivastava, Carlitz’s q-Bernoulli and q-Euler numbers and polynomials and a class of generalized q-Hurwitz zeta functions, Applied Mathematics and Computation, Vol. 215, Issue 3, October (2009), pp. 1185–1208.
  • [5] J. Choi, P. J. Anderson and H. M. Srivastava, Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz Zeta function, Applied Mathematics and Computation, 199 (2008), 723-737.
  • [6] U. Duran, M. Acikgoz, S. Araci, Symmetric identities involving weighted q-Genocchi polynomials under S4, Proceedings of the Jangjeon Mathematical Society,18 (2015), No. 4, pp 455-465.
  • [7] T. Kim, q-Volkenborn integration, Russian Journal of Mathematical Physics 9.3 (2002), pp. 288-299.
  • [8] T. Kim, On the weighted q-Bernoulli numbers and polynomials, Advances Studies Contemporary Mathematics, 21 (2011), no. 2, 231-236.
  • [9] B. A. Kupershmidt, Reflection Symmetries of q-Bernoulli Polynomials, Journal of Nonlinear Mathematical Physics, 12 (Suppl. 1), 412-422 (2005).
  • [10] Q.-M. Luo, H. M. Srivastava, q-extension of some relationships between the Bernoulli and Euler polynomials, Taiwanese Journal of Mathematics, Vol. 15, No. 1 (2011), pp. 241-257.
  • [11] N. I. Mahmudov, On a class of q-Benoulli and q-Euler polynomials, Advance in Difference Equations., (2013) 2013:108.
  • [12] C. S. Ryoo, Symmetric identities for Carlitz’s generalized twisted q-Bernoulli numbers and polynomials associated with p-adic q-integral on Zp, International Mathematical Forum, Vol. 10 (2015), no. 9, 435-441.
  • [13] H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Applied Mathematics & Information Sciences. 5 (2011), 390-444.
  • [14] H. M. Srivastava, T. Kim, Y. Simsek q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, Russian Journal of Mathematical Physics, 12 (2005), 241-268

New symmetric identities involving generalized Carlitz’s twisted q-Bernoulli polynomials under S_5

Yıl 2016, Cilt: 4 Sayı: 2, 52 - 57, 30.10.2016

Ugur Duran , Mehmet Acikgoz

https://doi.org/10.36753/mathenot.421455

Öz


Anahtar Kelimeler

Symmetric identities Generalized Carlitz’s twisted q-Bernoulli polynomials p-adic q-integral on Zp Invariant under S_5

Kaynakça

  • [1] T. M. Apostol, Introduction to Analytic Number Theory, New York; Splinger-Verlag, (1976).
  • [2] M. Acikgoz, S. Araci, U.Duran, New extensions of some known special polynomials under the theory of multiple q-calculus, Turkish Journal of Analysis and Number Theory, Vol. 3, No. 5, (2015) pages 128-139.
  • [3] S. Araci, U. Duran, M. Acikgoz, Symmetric identities involving q-Frobenius-Euler polynomials under Sym (5), Turkish Journal of Analysis and Number Theory, Vol. 3, No. 3, pp. 90-93 (2015).
  • [4] J. Choi, P. J. Anderson, H. M. Srivastava, Carlitz’s q-Bernoulli and q-Euler numbers and polynomials and a class of generalized q-Hurwitz zeta functions, Applied Mathematics and Computation, Vol. 215, Issue 3, October (2009), pp. 1185–1208.
  • [5] J. Choi, P. J. Anderson and H. M. Srivastava, Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz Zeta function, Applied Mathematics and Computation, 199 (2008), 723-737.
  • [6] U. Duran, M. Acikgoz, S. Araci, Symmetric identities involving weighted q-Genocchi polynomials under S4, Proceedings of the Jangjeon Mathematical Society,18 (2015), No. 4, pp 455-465.
  • [7] T. Kim, q-Volkenborn integration, Russian Journal of Mathematical Physics 9.3 (2002), pp. 288-299.
  • [8] T. Kim, On the weighted q-Bernoulli numbers and polynomials, Advances Studies Contemporary Mathematics, 21 (2011), no. 2, 231-236.
  • [9] B. A. Kupershmidt, Reflection Symmetries of q-Bernoulli Polynomials, Journal of Nonlinear Mathematical Physics, 12 (Suppl. 1), 412-422 (2005).
  • [10] Q.-M. Luo, H. M. Srivastava, q-extension of some relationships between the Bernoulli and Euler polynomials, Taiwanese Journal of Mathematics, Vol. 15, No. 1 (2011), pp. 241-257.
  • [11] N. I. Mahmudov, On a class of q-Benoulli and q-Euler polynomials, Advance in Difference Equations., (2013) 2013:108.
  • [12] C. S. Ryoo, Symmetric identities for Carlitz’s generalized twisted q-Bernoulli numbers and polynomials associated with p-adic q-integral on Zp, International Mathematical Forum, Vol. 10 (2015), no. 9, 435-441.
  • [13] H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Applied Mathematics & Information Sciences. 5 (2011), 390-444.
  • [14] H. M. Srivastava, T. Kim, Y. Simsek q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, Russian Journal of Mathematical Physics, 12 (2005), 241-268
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Ugur Duran

Mehmet Acikgoz

Yayımlanma Tarihi 30 Ekim 2016
Gönderilme Tarihi 15 Mart 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

APA Duran, U., & Acikgoz, M. (2016). New symmetric identities involving generalized Carlitz’s twisted q-Bernoulli polynomials under S_5. Mathematical Sciences and Applications E-Notes, 4(2), 52-57. https://doi.org/10.36753/mathenot.421455
AMA Duran U, Acikgoz M. New symmetric identities involving generalized Carlitz’s twisted q-Bernoulli polynomials under S_5. Math. Sci. Appl. E-Notes. Ekim 2016;4(2):52-57. doi:10.36753/mathenot.421455
Chicago Duran, Ugur, ve Mehmet Acikgoz. “New Symmetric Identities Involving Generalized Carlitz’s Twisted Q-Bernoulli Polynomials under S_5”. Mathematical Sciences and Applications E-Notes 4, sy. 2 (Ekim 2016): 52-57. https://doi.org/10.36753/mathenot.421455.
EndNote Duran U, Acikgoz M (01 Ekim 2016) New symmetric identities involving generalized Carlitz’s twisted q-Bernoulli polynomials under S_5. Mathematical Sciences and Applications E-Notes 4 2 52–57.
IEEE U. Duran ve M. Acikgoz, “New symmetric identities involving generalized Carlitz’s twisted q-Bernoulli polynomials under S_5”, Math. Sci. Appl. E-Notes, c. 4, sy. 2, ss. 52–57, 2016, doi: 10.36753/mathenot.421455.
ISNAD Duran, Ugur - Acikgoz, Mehmet. “New Symmetric Identities Involving Generalized Carlitz’s Twisted Q-Bernoulli Polynomials under S_5”. Mathematical Sciences and Applications E-Notes 4/2 (Ekim 2016), 52-57. https://doi.org/10.36753/mathenot.421455.
JAMA Duran U, Acikgoz M. New symmetric identities involving generalized Carlitz’s twisted q-Bernoulli polynomials under S_5. Math. Sci. Appl. E-Notes. 2016;4:52–57.
MLA Duran, Ugur ve Mehmet Acikgoz. “New Symmetric Identities Involving Generalized Carlitz’s Twisted Q-Bernoulli Polynomials under S_5”. Mathematical Sciences and Applications E-Notes, c. 4, sy. 2, 2016, ss. 52-57, doi:10.36753/mathenot.421455.
Vancouver Duran U, Acikgoz M. New symmetric identities involving generalized Carlitz’s twisted q-Bernoulli polynomials under S_5. Math. Sci. Appl. E-Notes. 2016;4(2):52-7.

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