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Open AccessArticle

Truncated-Exponential-Based Appell-Type Changhee Polynomials

1
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2
Department of Mathematics, SAS, Vellore Institute of Technology (VIT) Vellore, Tamil Nadu 632014, India
3
Department of Mathematics, Dongguk University, Gyeongju 38066, Korea
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(10), 1588; https://doi.org/10.3390/sym12101588
Received: 29 July 2020 / Revised: 7 September 2020 / Accepted: 21 September 2020 / Published: 24 September 2020
(This article belongs to the Special Issue Symmetry and IoT Intelligence in the Post Pandemic Economy)
The truncated exponential polynomials em(x) (1), their extensions, and certain newly-introduced polynomials which combine the truncated exponential polynomials with other known polynomials have been investigated and applied in various ways. In this paper, by incorporating the Appell-type Changhee polynomials Chn*(x) (10) and the truncated exponential polynomials in a natural way, we aim to introduce so-called truncated-exponential-based Appell-type Changhee polynomials eCn*(x) in Definition 1. Then, we investigate certain properties and identities for these new polynomials such as explicit representation, addition formulas, recurrence relations, differential and integral formulas, and some related inequalities. We also present some integral inequalities involving these polynomials eCn*(x). Further we discuss zero distributions of these polynomials by observing their graphs drawn by Mathematica. Lastly some open questions are suggested. View Full-Text
Keywords: Changhee polynomials and numbers; Appell-type Changhee polynomials and numbers; truncated-exponential polynomials; truncated-exponential-based Appell-type Changhee polynomials and numbers; zero distributions; Newton–Raphson’s theorem Changhee polynomials and numbers; Appell-type Changhee polynomials and numbers; truncated-exponential polynomials; truncated-exponential-based Appell-type Changhee polynomials and numbers; zero distributions; Newton–Raphson’s theorem
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Nahid, T.; Alam, P.; Choi, J. Truncated-Exponential-Based Appell-Type Changhee Polynomials. Symmetry 2020, 12, 1588.

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