N. U. Khan, T. Kim and T. Usman

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 2, Pages 76-90

DOI: 10.7546/nntdm.2019.25.2.76-90

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## Details

### Authors and affiliations

N. U. Khan

*Department of Applied Mathematics, Faculty of Engineering and Technology
Aligarh Muslim University, Aligarh-202002, India
*

T. Kim

*Department of Mathematics, College of Natural Science
Kwangwoon University, Seoul 139-704, S. Korea
*

T. Usman

*Department of Applied Mathematics, Faculty of Engineering and Technology
Aligarh Muslim University, Aligarh-202002, India
*

### Abstract

In the past years, many researchers have worked on degenerate polynomials and a variety of its extentions and variants can be found in literature. Following up, in this article, we firstly introduce the partially degenerate Legendre–Genocchi polynomials, and further define a new generalization of degenerate Legendre–Genocchi polynomials. From our generalization, we establish some implicit summation formulae and symmetry identities by the generating function of partially degenerate Legendre–Genocchi polynomials. Eventually, it can be found that some recently demonstrated summations and identities stated in the article, are special cases of our results.

### Keywords

- Legendre polynomials
- Partially degenerate Genocchi polynomials
- Partially degen-erate Legendre–Genocchi polynomials
- Summation formula
- Symmetric identities

### 2010 Mathematics Subject Classification

- 33B15
- 33C10
- 33C15

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## Cite this paper

APAKhan, N. U., Kim, T. & Usman, T. (2019). A note on partially degenerate Legendre–Genocchi polynomials. Notes on Number Theory and Discrete Mathematics, 25(2), 76-90, doi: 10.7546/nntdm.2019.25.2.76-90.

ChicagoKhan, N. U., Kim, T. & Usman, T. “A note on partially degenerate Legendre–Genocchi polynomials.” Notes on Number Theory and Discrete Mathematics 25, no. 2 (2019): 76-90, doi: 10.7546/nntdm.2019.25.2.76-90.

MLAKhan, N. U., Kim, T. & Usman, T. “A note on partially degenerate Legendre–Genocchi polynomials.” Notes on Number Theory and Discrete Mathematics 25.2 (2019): 76-90. Print, doi: 10.7546/nntdm.2019.25.2.76-90.