Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials

Lee Chae Jang

doi:doi:10.11648/j.acm.20170606.13

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Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials

Lee Chae Jang

Published in Applied and Computational Mathematics (Volume 6, Issue 6)

Received: 25 July 2017 Accepted: 10 November 2017 Published: 15 December 2017

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Abstract

Recently, Kim-Kim (2016-2017) studied simmetric identities of higher-order degenerate Bernoulli and Euler polynomials which were defined by Carlitz (1979). In this paper, we define the higher-order deformed degenerate Bernoulli and Euler polynomials which are modified the higher-order degenerate Bernoulli and Euler polynomials. We also investigate some interesting identities for the the higher-order deformed degenerate Bernoulli and Euler polynomials.

Published in	Applied and Computational Mathematics (Volume 6, Issue 6)
DOI	10.11648/j.acm.20170606.13
Page(s)	254-258
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Bernoulli Polynomials, Euler Polynomials, Degenerate Bernoulli Polynomials

References

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[13]	D. V. Dolgy, T. Kim, J. J. Seo, On the symmetric identities of modified degenerate Bernoulli polynomials, Proc. Jangjeon Math. Soc., 19(2) (2016), 301-308.
[14]	H. I. Kwon, T. Kim, J. J. Seo, Some new identities of symmetry for modified degenerate Euler polynomials, Proc. Jangjeon Math. Soc., 19(2) (2016), 237-242.
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Lee Chae Jang. (2017). Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials. Applied and Computational Mathematics, 6(6), 254-258. https://doi.org/10.11648/j.acm.20170606.13

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ACS Style

Lee Chae Jang. Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials. Appl. Comput. Math. 2017, 6(6), 254-258. doi: 10.11648/j.acm.20170606.13

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AMA Style

Lee Chae Jang. Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials. Appl Comput Math. 2017;6(6):254-258. doi: 10.11648/j.acm.20170606.13

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@article{10.11648/j.acm.20170606.13,
  author = {Lee Chae Jang},
  title = {Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {6},
  pages = {254-258},
  doi = {10.11648/j.acm.20170606.13},
  url = {https://doi.org/10.11648/j.acm.20170606.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170606.13},
  abstract = {Recently, Kim-Kim (2016-2017) studied simmetric identities of higher-order degenerate Bernoulli and Euler polynomials which were defined by Carlitz (1979). In this paper, we define the higher-order deformed degenerate Bernoulli and Euler polynomials which are modified the higher-order degenerate Bernoulli and Euler polynomials. We also investigate some interesting identities for the the higher-order deformed degenerate Bernoulli and Euler polynomials.},
 year = {2017}
}

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TY  - JOUR
T1  - Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials
AU  - Lee Chae Jang
Y1  - 2017/12/15
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170606.13
DO  - 10.11648/j.acm.20170606.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 254
EP  - 258
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170606.13
AB  - Recently, Kim-Kim (2016-2017) studied simmetric identities of higher-order degenerate Bernoulli and Euler polynomials which were defined by Carlitz (1979). In this paper, we define the higher-order deformed degenerate Bernoulli and Euler polynomials which are modified the higher-order degenerate Bernoulli and Euler polynomials. We also investigate some interesting identities for the the higher-order deformed degenerate Bernoulli and Euler polynomials.
VL  - 6
IS  - 6
ER  -

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Author Information

Lee Chae Jang

Graduate School of Education, Konkuk University, Seoul, Republic of Korea

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Lee Chae Jang. (2017). Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials. Applied and Computational Mathematics, 6(6), 254-258. https://doi.org/10.11648/j.acm.20170606.13

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ACS Style

Lee Chae Jang. Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials. Appl. Comput. Math. 2017, 6(6), 254-258. doi: 10.11648/j.acm.20170606.13

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AMA Style

Lee Chae Jang. Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials. Appl Comput Math. 2017;6(6):254-258. doi: 10.11648/j.acm.20170606.13

Copy | Download

@article{10.11648/j.acm.20170606.13,
  author = {Lee Chae Jang},
  title = {Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {6},
  pages = {254-258},
  doi = {10.11648/j.acm.20170606.13},
  url = {https://doi.org/10.11648/j.acm.20170606.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170606.13},
  abstract = {Recently, Kim-Kim (2016-2017) studied simmetric identities of higher-order degenerate Bernoulli and Euler polynomials which were defined by Carlitz (1979). In this paper, we define the higher-order deformed degenerate Bernoulli and Euler polynomials which are modified the higher-order degenerate Bernoulli and Euler polynomials. We also investigate some interesting identities for the the higher-order deformed degenerate Bernoulli and Euler polynomials.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials
AU  - Lee Chae Jang
Y1  - 2017/12/15
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170606.13
DO  - 10.11648/j.acm.20170606.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 254
EP  - 258
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170606.13
AB  - Recently, Kim-Kim (2016-2017) studied simmetric identities of higher-order degenerate Bernoulli and Euler polynomials which were defined by Carlitz (1979). In this paper, we define the higher-order deformed degenerate Bernoulli and Euler polynomials which are modified the higher-order degenerate Bernoulli and Euler polynomials. We also investigate some interesting identities for the the higher-order deformed degenerate Bernoulli and Euler polynomials.
VL  - 6
IS  - 6
ER  -

Copy | Download