A note on partially degenerate Legendre–Genocchi polynomials

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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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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APA

Khan, 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.

Chicago

Khan, 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.

MLA

Khan, 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.

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