Some explicit identities for the modified higher-order degenerate q-Euler polynomials and their zeroes

Volume 10, Issue 5, pp 2524--2538 http://dx.doi.org/10.22436/jnsa.010.05.21

Publication Date: May 25, 2017 Submission Date: October 20, 2016

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Authors

L. C. Jang - Graduate School of Education, Konkuk University, Seoul 143-701, Republic of Korea. B. M. Kim - Department of Mechanical System Engineering, Dongguk University, Gyeongju, 780-714, Korea. S. K. Choi - Department of Mathematics Education, Konkuk University, Seoul 143-701, Republic of Korea. C. S. Ryoo - Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea. D. V. Dolgy - Hanrimwon, Kwangwoon University, Seoul 139-701, Republic of Korea. - Institute of Natural Sciences, Far eastern Federal University, Vladivostok 690950, Russia.

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.

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Keywords

• Identities of symmetry
• modified q-Euler polynomials
• modified higher-order degenerate q-Euler polynomials.

MSC

•  11B68
•  11S80
•  05A19
•  05A30

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