Some identities involving degenerate Cauchy numbers and polynomials of the fourth kind
Keywords:
Cauchy polynomials, Generating functions, Riordan matrix, Degenerate Cauchy polynomials of the fourth kind, Stirling numbers, Lab numbers, Bell numbers, Daehee numbers.
Abstract
In this paper, we study the constant equations associated with the degenerate Cauchy polynomials of the fourth kind using the generating function and Riordan array. By using the generating function method and the Riordan array method, we establish some new constants between the degenerate Cauchy polynomials of the fourth kind and two types of Stirling numbers, Lab numbers, two types of generalized Bell numbers, Daehee numbers, Bernoulli numbers and polynomials.
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References
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[8] D. Lim, Degenerate, partially degenerate and totally degenerate Daehee numbers and polynomials, Advances in Difference Equations 1 (2015), 1–14.
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[2] Pyo S S, Degenerate Cauchy numbers and polynomials of the fourth kind, Advanced Studies in Contemporary Mathematics, 28 (2018), 127–138.
[3] Qi F, An integral representation, complete monotonicity, and inequalities of Cauchy numbers of the second kind, Journal of Number Theory, 144 (2014), 244–255.
[4] Kim T, On the degenerate Cauchy numbers and polynomials, Proc. Jangjeon Math, 18 (2015), 307–312.
[5] Kim T, Degenerate Cauchy numbers and polynomials of the second kind, Advanced Studies in Contemporary Mathematics, 27 (2017), 441–449.
[6] Pyo S S, Kim T ,and Rim S H, Degenerate Cauchy numbers of the third kind, Journal of Inequalities and Applications 32 (2018), 1–12.
[7] Kumar Sharma S, Khan W A, Araci S, et al. New type of degenerate Daehee polynomials of the second kind, Advances in Difference Equations, 1 (2020), 1–14.
[8] D. Lim, Degenerate, partially degenerate and totally degenerate Daehee numbers and polynomials, Advances in Difference Equations 1 (2015), 1–14.
[9] Yanhong Li, Wuyungaowa, Some identities involving the Λ-Daehee numbers and polynomials, Journal of Progressive Research in Mathematics, 16 (2020),2395-0218.
[10] Wang W, Riordan arrays and harmonic number identities, Computers Mathematics with Applications, 60 (2010), 1494–1509.
Published
2023-06-27
How to Cite
Tian, X.-Q., & ., W. (2023). Some identities involving degenerate Cauchy numbers and polynomials of the fourth kind. Journal of Progressive Research in Mathematics, 20(1), 136-152. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/2203
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