[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
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
1.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):52-57. doi:10.36753/mathenot.421455
Chicago
Duran, Ugur, and Mehmet Acikgoz. 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.
EndNote
Duran U, Acikgoz M (October 1, 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
[1]U. Duran and M. Acikgoz, “New symmetric identities involving generalized Carlitz’s twisted q-Bernoulli polynomials under S_5”, Math. Sci. Appl. E-Notes, vol. 4, no. 2, pp. 52–57, Oct. 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 (October 1, 2016): 52-57. https://doi.org/10.36753/mathenot.421455.
JAMA
1.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, and Mehmet Acikgoz. “New Symmetric Identities Involving Generalized Carlitz’s Twisted Q-Bernoulli Polynomials under S_5”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 2, Oct. 2016, pp. 52-57, doi:10.36753/mathenot.421455.
Vancouver
1.Ugur Duran, Mehmet Acikgoz. New symmetric identities involving generalized Carlitz’s twisted q-Bernoulli polynomials under S_5. Math. Sci. Appl. E-Notes. 2016 Oct. 1;4(2):52-7. doi:10.36753/mathenot.421455
