Abstract
By the same motivation Kim et al. (Adv Stud Theor Phys 8:745–754, 2014), the main aim of this paper is to define some new mixed type polynomials with connected to Boole and Tangent polynomials. Also, we obtain new and interesting identities from these polynomials.
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Açíkgöz, M., Araci, S.: On the generating function for Bernstein polynomials. In: ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP Conference Proceedings, vol. 1281, Issue 1, pp. 1141–1143. doi:10.1063/1.3497855
Araci, S., Ağyüz, E., Acikgoz, M.: On a q-analog of some numbers and polynomials. J. Inequal. Appl. 2015, 19 (2015). doi:10.1186/s13660-014-0542-y
Araci, S., Acikgoz, M., Park, K.H., Jolany, H.: On the unification of two families of multiple twisted type polynomials by using \(p\)-Adic \(q\)-integral at \(q=-1\). Bull. Malays. Math. Sci. Soc. (2) 37(2), 543–554 (2014)
Araci, S., Acikgoz, M., Şen, E.: On the extended Kim’s p-adic q-deformed fermionic integrals in the \(p\)-adic integer ring. J. Number Theory 133, 3348–3361 (2013)
Kim, D.S., Kim, T., Lee, S.-H., Seo, J.-J.: Higher-order Daehee numbers and polynomials. Int. J. Math. Anal. 8(5–6), 273–283 (2014)
Kim, D.S., Kim, T., Seo, J.-J., Lee, S.-H.: Higher-order Changhee numbers and polynomials. Adv. Stud. Theor. Phys. 8(8), 365–373 (2014)
Kim, T.: q-Volkenborn integration. Russ. J. Math. Phys. 9(3), 288–299 (2002)
Kim, T.: Barnes-type multiple q-zeta functions and q-Euler polynomials. J. Phys. A Math. Theor. 43, 255201 (2010). p. 11
Kim, D.S., Kim, T., Kwon, H.I.: Identities of some special mixed-type polynomials. Adv. Stud. Theor. Phys. 8(17), 745–754 (2014)
Kim, D.S., Kim, T.: A note on the Boole polynomials. Integral Transform. Special Function. 25(8), 627–633 (2014)
Kim, D.S., Jang, Y.S., Kim, T., Rim, S.H.: A note on the Boole polynomials with q-parameter. arXiv:1407.2957
Kim, D.S., Kim, T., Seo, J.J.: A note on q- analogue of Boole polynomials. arXiv:1403.4447
Roman, S.: The Umbral Calculus, Pure and Applied Mathematics, vol. 111. Academic Press Inc. [Harcourt Brace Jovanovich, Publishers], New York (1984)
Comtet L.: Advanced combinatorics, enlarged ed., D. Reidel Publishing Co., Dordrecht. The art of finite and infinite expansions (1974)
Andrews, G.E., Askey, R., Roy, R.: Special Functions. Encyclopedia of Mathematics and Its Applications, vol. 71. Cambridge University Press, Cambridge (1999)
Horadam A.F.: Genocchi polynomials. Proceedings of the fourth International Conference on Fibonacci Numbers and Their Applications. Kluwer, pp. 145–66 (1991)
Carlitz, L.: Multiplication formulas for products of Bernoulli and Euler polynomials. Pac. J. Math. 9(3), 661–666 (1959)
Carlitz, L.: q-Bernoulli numbers and polynomials. Duke Math. J. 15(4), 987–1000 (1948)
Fort, T.: Finite Differences. Oxford University Press, Oxford (1948)
Simsek, Y., Acikgoz, M.: A new generating function of q -Berstein-type polynomials and their interpolation function. Abstr. Appl. Anal. (2010). doi:10.1155/2010/769095
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Gurkan, F.G., Acıkgoz, M. & Agyuz, E. A study on the new mixed-type polynomials related to Boole polynomials. Afr. Mat. 28, 279–290 (2017). https://doi.org/10.1007/s13370-016-0446-8
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DOI: https://doi.org/10.1007/s13370-016-0446-8