A Note on Modified Degenerate Changhee–Genocchi Polynomials of the Second Kind
Abstract
1. Introduction
2. Modified Degenerate Changhee–Genocchi Polynomials of the Second Kind
3. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
- Alatawi, M.S.; Khan, W.A. New type of degenerate Changhee-Genocchi polynomials. Axioms 2022, 11, 355. [Google Scholar] [CrossRef]
- Khan, W.A.; Alatawi, M.S. Analytical properties of degenerate Genocchi polynomials the second kind and some of their applications. Symmetry 2022, 14, 1500. [Google Scholar] [CrossRef]
- Sharma, S.K.; Khan, W.A.; Araci, S.; Ahmed, S.S. New type of degenerate Daehee polynomials of the second kind. Adv. Differ. Equ. 2020, 2020, 428. [Google Scholar] [CrossRef]
- Khan, W.A. A note on q-analogue of degenerate Catalan numbers associated with p-adic integral on . Symmetry 2022, 14, 1119. [Google Scholar] [CrossRef]
- Khan, W.A. A study on q-analogue of degenerate -Changhee numbers and polynomials. South East Asian Math. Math. Sci. 2022, 18, 71–82. [Google Scholar]
- Khan, W.A.; Haroon, H. Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials. SpringerPlus 2016, 5, 1920. [Google Scholar] [CrossRef] [PubMed]
- Khan, W.A.; Alatawi, M.S.; Duran, U. A note on degenerate Catalan-Daehee numbers and polynomials. Symmetry 2022, 14, 2169. [Google Scholar] [CrossRef]
- Khan, W.A.; Younis, J.; Duran, U.; Iqbal, A. The higher-order type 2 Daehee polynomials associated with p-adic integral on . Appl. Math. Sci. Eng. 2022, 30, 573–582. [Google Scholar] [CrossRef]
- Khan, W.A.; Nisar, K.S.; Duran, U.; Acikgoz, M.; Araci, S. Multifarious implicit summation formulae of Hermite-based poly-Daehee polynomials. Appl. Math. Inf. Sci. 2018, 12, 305–310. [Google Scholar] [CrossRef]
- Kim, B.M.; Jang, L.-C.; Kim, W.; Kwon, H.I. Degenerate Changhee-Genocchi numbers and polynomials. J. Ineq. Appl. 2017, 2017, 294. [Google Scholar] [CrossRef]
- Kim, D.S.; Kim, T. Higher-order Bernoulli and poly-Bernoulli mixed type polynomials. Georgian Math. J. 2015, 22, 265–272. [Google Scholar] [CrossRef][Green Version]
- Khan, W.A.; Kamarujjama, D. Construction of partially degenerate Bell-Bernoulli polynomials of the first kind and their certain properties. Analysis 2022, 42, 171–184. [Google Scholar] [CrossRef]
- Khan, W.A.; Haroon, H. Higher order degenerate Hermite-Bernoulli polynomials arising from p-adic integrals on . Iran. J. Math. Sci. Inform. 2022, 17, 171–189. [Google Scholar]
- Kim, D.S.; Kim, T.; Seo, J. A note on Changhee polynomials and numbers. Adv. Stud. Theor. Phys. 2013, 7, 993–1003. [Google Scholar] [CrossRef]
- Kwon, H.-I.; Kim, T.; Park, J.W. A note on degenerate Changhee-Genocchi polynomials and numbers. Glob. J. Pure Appl. Mat. 2016, 12, 4057–4064. [Google Scholar]
- Kim, B.-M.; Jeong, J.; Rim, S.-H. Some explicit identities on Changhee-Genocchi polynomials and numbers. Adv. Differ. Equ. 2016, 2016, 202. [Google Scholar] [CrossRef]
- Kim, Y.; Kwon, J.; Sohn, G.; Lee, J.G. Some identities of the partially degenerate Changhee-Genocchi polynomials and numbers. Adv. Stud. Contemp. Math. 2019, 29, 537–550. [Google Scholar]
- Kim, D.S.; Kim, T. Daehee numbers and polynomials. Appl. Math. Sci. 2013, 120, 5969–5976. [Google Scholar] [CrossRef]
- Kim, T.; Kim, D.S.; Seo, J.J.; Kwon, H.I. Differential equations associated with λ-Changhee polynomials. J. Nonlinear Sci. Appl. 2016, 9, 3098–3111. [Google Scholar] [CrossRef][Green Version]
- Pathan, M.A.; Khan, W.A. On a class of generalized Humbert-Hermite polynomials via generalized Fibonacci polynomials. Turk. J. Math. 2022, 46, 929–945. [Google Scholar] [CrossRef]
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Khan, W.A.; Alatawi, M.S. A Note on Modified Degenerate Changhee–Genocchi Polynomials of the Second Kind. Symmetry 2023, 15, 136. https://doi.org/10.3390/sym15010136
Khan WA, Alatawi MS. A Note on Modified Degenerate Changhee–Genocchi Polynomials of the Second Kind. Symmetry. 2023; 15(1):136. https://doi.org/10.3390/sym15010136
Chicago/Turabian StyleKhan, Waseem Ahmad, and Maryam Salem Alatawi. 2023. "A Note on Modified Degenerate Changhee–Genocchi Polynomials of the Second Kind" Symmetry 15, no. 1: 136. https://doi.org/10.3390/sym15010136
APA StyleKhan, W. A., & Alatawi, M. S. (2023). A Note on Modified Degenerate Changhee–Genocchi Polynomials of the Second Kind. Symmetry, 15(1), 136. https://doi.org/10.3390/sym15010136