A note on the modified q-Genocchi numbers and polynomials with weight (α, β)

• Autorzy: Araci S. , Acikgoz M , Qi F. , Jolany H
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper concerns to establish modified q-Genocchi numbers and polynomials with weight (α,β). In this paper we investigate special generalized q-Genocchi polynomials and we apply the method of generating function, which are exploited to derive further classes of q-Genocchi polynomials and develop q-Genocchi numbers and polynomials. By using the Laplace-Mellin transformation integral, we define q-Zeta function with weight (α,β) and by presenting a link between q-Zeta function with weight (α,β) and q-Genocchi numbers with weight (α,β) we obtain an interpolation formula for the q-Genocchi numbers and polynomials with weight (α,β). Also we derive distribution formula (Multiplication Theorem) and Witt’s type formula for modified q-Genocchi numbers and polynomials with weight (α,β) which yields a deeper insight into the effectiveness of this type of generalizations for q-Genocchi numbers and polynomials. Our new generating function possess a number of interesting properties which we state in this paper.

Słowa kluczowe

EN

Genocchi numbers and polynomials; q-Genocchi numbers and polynomials; q-Genocchi numbers and polynomials with weight α.

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2013
• Tom: Nr 51
• Strony: 21--32
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Araci S.

• University of Gaziantep Faculty of Science and Arts Department of Mathematics 27310 Gaziantep, Turkey

autor

Acikgoz M

• University of Gaziantep Faculty of Science and Arts Department of Mathematics 27310 Gaziantep, Turkey

autor

Qi F.

• Department of Mathematics College of Science Tianjin Polytechnic University Tianjin 300160, China

autor

Jolany H

• School of Mathematics Statistics and Computer Science University of Tehran, Iran

Bibliografia

• [1] Araci S., Aslan N., Seo J-J., A note on the weighted Twisted Dirichlet’s type q-Euler numbers and polynomials, Honam Mathematical J., 33(3)(2011), 311-320.
• [2] Araci S., Acikgoz M., Seo J-J., A study on the weighted q-Genocchi numbers and polynomials with their Interpolation Function, Honam Mathematical J, 34(1)(2012), 11-18.
• [3] Araci S., Erdal D., Kang D-J., Some new properties on the q-Genocchi numbers and polynomials associated with q-Bernstein polynomials, Honam Mathematical J, 33(2)(2011), 261-270.
• [4] Araci S., Erdal D., Seo J-J., A study on the fermionic p-adic q-integral representation on Zp associated with weighted q-Bernstein and q-Genocchi polynomials, Abstract and Applied Analysis, Vol. 2011, Article ID 649248, 10 pages.
• [5] Araci S., Seo J-J., Erdal D., New construction weighted (h, q)-Genocchi numbers and polynomials related to zeta type functions, Discrete Dynamics in Nature and Society, Vol. 2011, Article ID 487490, 7 pages, doi:10.11 55/2011/487490.
• [6] Hwang K-W., Dolgy D-V., Lee S.H., Kim T., On the Higher-Order q- Euler numbers and polynomials with weight a, Discrete Dynamics in Nature and Society, (2011), Article ID 354329, 12 pages.
• [7] Jolany H., Araci S., Acikgoz M., Seo J-J., A note on the generalized q-Genochhi measures with weight alpha, Bol. Soc. Paran. Mat., 31(1)(2013), 17-27.
• [8] Kim T., On the weighted q-Bernoulli numbers and polynomials, Advanced Studies in Contemporary Mathematics, 21(2)(2011), 207-215, http://arxiv.org/abs/1011.5305.
• [9] Kim T., On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl., 326(2007), 1458-1465.
• [10] Kim T., On the multiple q-Genocchi and Euler numbers, Russian J. Math. Phys, 15(4)(2008), 481-486. arXiv:0801.0978v1[math.NT].
• [11] Kim T., The modified q-Euler numbers and polynomials, Advn. Stud. Con- temp. Math., 16(2008), 161-170.
• [12] Kim T., q-Volkenborn integration, Russ. J. Math. Phys., 9(2002), 288-299.
• [13] Kim T., q-Bernoulli numbers and polynomials associated with Gaussian bino- mial coefficients, Russ. J. Math. Phys., 15(2008), 51-57.
• [14] Kim T., An invariant p-adic q-integrals on Zp, Applied Mathematics Letters, 21(2008), 105-108.
• [15] Kim T., A note on the q-Genocchi Numbers and Polynomials, Journal of Inequalities and Applications, Article ID 71452, 8 pages, doi:10.1155/2007 /71452.
• [16] Kim T., q-Euler numbers and polynomials associated with p-adic q-integrals, J. Nonlinear Math. Phys., 14(1)(2007), 15-27.
• [17] Kim T., New approach to q-Euler polynomials of higher order, Russ. J. Math. Phys., 17(2)(2010).
• [18] 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(4)(2009), 484-491.
• [19] Kim T., Choi J., Kim Y.H., Ryoo C.S., A note on the weighted p-adic q- Euler measure on Zp, Advn. Stud. Contemp. Math., 21(2011), 35-40.
• [20] Kim T., Choi J., On the q-Bernoulli numbers and polynomials with weight a, Abstract and Applied Analysis, (2011), Article ID 392025, 14 pages.
• [21] Kim T., Choi J., Kim Y.H. and Jang L.C., On p-Adic Analogue of q-Bern- stein Polynomials and Related Integrals, Discrete Dynamics in Nature and Society, Article ID 179430, 9 pages, doi:10.1155/2010/179430.
• [22] KIM T., DOLGY D-V., LEE B., RIM S-H., Identities on the weighted q-Euler numbers of higher order, Discrete Dynamics in Nature and Society, (2011), Article ID 918364, 6 pages.
• [23] Kim T., Lee S.H., Dolgy D.V., Ryoo C.S., A note on the generalized q-Bernoulli measures with weight a, Abstract and Applied Analysis, Article ID 867217, 9 pages, doi:10.1155/2011/867217.
• [24] Ozden H., Simsek Y., Rim S-H., Cangul I-N., A note on p-adic q-Euler measure, Adv. Stud. Contemp. Math., 14(2007), 233-239.