# A NOTE ON THE WEIGHTED TWISTED DIRICHLET'S TYPE q-EULER NUMBERS AND POLYNOMIALS

• Araci, Serkan ;
• Aslan, Nurgul ;
• Se, Jong-Jin
• Accepted : 2011.06.07
• Published : 2011.09.25
• 37 13

#### Abstract

We in this paper construct Dirichlet's type twisted q-Euler numbers and polynomials with weight ${\alpha}$. We give some interestin identities some relations.

#### Keywords

Euler numbers and polynomials;q-Euler numbers and polynomials;Twisted q-Euler numbers and polynomials with weight ${\alpha}$;Dirihlet' type twisted q-Euler numbers and polynomials with weight ${\alpha}$

#### References

1. Araci, S. Erdal, D. and Seo, J.J., A Study on the The Weighted q-Genocchi Numbers and Polynomials Their Interpolation function, (Submitted)
2. Araci, S. Seo, J.J. and Erdal, D., Different Approach On The (h; q) Genocchi Numbers and Polynomials Associated with q-Bernstein Polynomials, (Submitted)
3. Kim, T., A New Approach to q-Zeta Function, Adv. Stud. Contemp. Math. 11 (2) 157-162.
4. Araci, S. Seo, J.J. and Erdal, D., New Construction weighted (h; q)-Genocchi numbers and Polynomials Related to Zeta Type Functions, Discrete Dynamics in Nature and Society(in press)
5. Kim, T., On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl. 326 (2007) 1458-1465. https://doi.org/10.1016/j.jmaa.2006.03.037
6. Kim, T., On the multiple q-Genocchi and Euler numbers, Russian J. Math. Phys. 15 (4) (2008) 481-486. arXiv:0801.0978v1 [math.NT] https://doi.org/10.1134/S1061920808040055
7. Kim, T., On the weighted q-Bernoulli numbers and polynomials, Advanced Studies in Contemporary Mathematics 21(2011), no.2, p. 207-215, http://arxiv.org/abs/1011.5305.
8. Kim, T., A Note on the q-Genocchi Numbers and Polynomials, Journal of Inequalities and Applications 2007 (2007) doi:10.1155/2007/71452. Article ID 71452, 8 pages. https://doi.org/10.1155/2007/71452
9. Kim, T., q-Volkenborn integration, Russ. J. Math. phys. 9(2002) ; 288-299.
10. Kim, T., An invariant p-adic q-integrals on Zp, Applied Mathematics Letters, vol. 21, pp. 105-108, 2008. https://doi.org/10.1016/j.aml.2006.11.011
11. Kim, T., q-Euler numbers and polynomials associated with p-adic q-integrals, J. Nonlinear Math. Phys., 14 (2007), no. 1, 15-27. https://doi.org/10.2991/jnmp.2007.14.1.3
12. Kim, T., New approach to q-Euler polynomials of higher order, Russ. J. Math. Phys., 17 (2010), no. 2, 218-225. https://doi.org/10.1134/S1061920810020068
13. 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. https://doi.org/10.1134/S1061920809040037
14. Kim, T. and Rim, S.-H., On the twisted q-Euler numbers and polynomials associated with basic q-l-functions, Journal of Mathematical Analysis and Applications, vol. 336, no. 1, pp. 738-744, 2007. https://doi.org/10.1016/j.jmaa.2007.03.035
15. T. Kim, On p-adic q-l-functions and sums of powers, J. Math. Anal. Appl. (2006), doi:10.1016/j.jmaa.2006.07.071 https://doi.org/10.1016/j.jmaa.2006.07.071
16. Park. Kyoung Ho., On Interpolation Functions of the Generalized Twisted (h; q)-Euler Polynomials, Journal of Inequalities and Applications., Volume 2009, Article ID 946569, 17 pages
17. Jang. L.-C., On a q-analogue of the p-adic generalized twisted L-functions and p-adic q-integrals, Journal of the Korean Mathematical Society, vol. 44, no. 1, pp. 1-10, 2007. https://doi.org/10.4134/JKMS.2007.44.1.001
18. Ryoo. C. S., A note on the weighted q-Euler numbers and polynomials, Advan. Stud. Contemp. Math. 21(2011), 47-54.
19. Ryoo. C. S, Lee. H. Y, and Jung. N. S., A note on the twisted q-Euler numbers and polynomials with weight ${\alpha}$, (Communicated).
20. Y. Simsek, Theorems on twisted L-function and twisted Bernoulli numbers, Advan. Stud. Contemp. Math., 11(2005), 205-218.
21. Y. Simsek, Twisted (h; q)-Bernoulli numbers and polynomials related to twisted (h; q)-zeta function and L-function, J. Math. Anal. Appl., 324(2006), 790-804. https://doi.org/10.1016/j.jmaa.2005.12.057
22. Y. Simsek, On p-Adic Twisted q-L-Functions Related to Generalized Twisted Bernoulli Numbers, Russian J. Math. Phys., 13(3)(2006), 340-348. https://doi.org/10.1134/S1061920806030095
23. Dolgy, D-V., Kang, D-J., Kim, T., and Lee, B., Some new identities on the twisted (h; q)-Euler numbers q-Bernstein polynomials, arXiv: 1105.0093.

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