Author/Authors :
Jang ، L. C. - Konkuk University , Kim ، B. M. - Dongguk University , Choi ، S. K. - Konkuk University , Ryoo ، C. S. - Hannam University , Dolgy ، D. V. Kwangwoon University
Abstract :
Recently, Kim et al. [D. S. Kim, T. Kim, Ars Combin., 126 (2016), 435–441], [D. S. Kim, T. Kim, J. Nonlinear Sci. Appl., 9 (2016), 443–451], [T. Kim, D. S. Kim, H.-I. Kwon, Filomat, 30 (2016), 905–912] and [T. Kim, D. S. Kim, H.-I. Kwon, J.-J. Seo, D. V. Dolgy, J. Nonlinear Sci. Appl., 9 (2016), 1077–1082] studied symmetric identities of higher-order degenerate q-Euler polynomials. In this paper, we define the modified higher-order degenerate q-Euler polynomials and give some identities for these polynomials. Also we give numerical investigations of the zeroes of the modified higher-order q-Euler polynomials and the zeroes of the modified higher-order degenerate q-Euler polynomials. Furthermore, we demonstrate the shapes and zeroes of the modified higher-order q-Euler polynomials and the modified higher-order degenerate q-Euler polynomials by using a computer.
Keywords :
Identities of symmetry , modified q , Euler polynomials , modified higher , order degenerate q , Euler polynomials
