Combinatorial Identities with Several Kinds of Degenerate-Daehee Sequences

  • Tian Hao Department of Mathematical Sciences, Inner Mongolia University, 235 West Daxue Road, Inner Mongolia, China
  • . Wuyungaowa Department of Mathematical Sciences, Inner Mongolia University, 235 West Daxue Road, Inner Mongolia, China
Keywords: Moment, Generating function, Degenerate Daehee numbers of the third kind, Uniform distribution, Gamma distribution.

Abstract

In this paper, we mainly make use of the probabilistic method to calculate several different moment representations of the degenerate Daehee numbers of the third kind with degenerate log function. We also obtain the moment expressions of the degenerate Daehee numbers of higher-order and degenerate Daehee numbers of the second kind. When deriving the moment representations of degenerate Stirling numbers and the degenerate Bernoulli numbers, we arrive at the combinatorial identities of relationships of them and we prove them by the probabilistic method.

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References

1. Carlitz. L: Extended Stirling and exponential numbers. Duke Mathematical Journal,32(2):205C224, 1965.
2. El-Desouky. B.S., Mustafa. A.: New Results on Higher-order Daehee and Bernoulli Numbers and Polynomials. Advances in Difference Equations,(32), 2016.
3. Jang G.W., Kwon J., Lee. J.G.: Some Identities of Degenerate Daehee Numbers Arising from Nonlinear Differential Equation. Advances in Difference Equations,(206), 2017.
4. Kim D.S., Kim T., Kwon H.I., Dolgy. D.V.: A Note on Degenerate Bernoulli Numbers and Polynomials Associated with P-adic Invariant Integral on Zp. Applied Mathematics and Computation, 295:198C204, 2015.
5. Kim D.S., Kim T., Kwon H.I.,, Jang G.W.: Degenerate Daehee Polynomials of the Second Kind. Proceedings of the Jangjeon Mathematical Society, 21(1):83C97, 2018.
6. Kim T.: On the Degenerate Cauchy Numbers and Polynomials. Proceedings of the Jangjeon Mathematical Society, 18(3):307C312, 2015.
7. Kim T., Kim D.S., Kwon H.I.: A Note on Degenerate Stirling Numbers and Their Applications. Proceedings of the Jangjeon Mathematical Society, 21(2):195C203, 2018.
8. Liu C., Wuyungaowa: Application of Probabilistic Method on Daehee Sequences. European Journal of Pure and Applied Mathematics, 11(1):69C78, 2018.
9. Pro S.S., Kim T., RIM S.H.: Identities of the Degenerate Daehee Numbers with the Bernoulli Numbers of the Second Kind Arising from Nonlinear Differential Equation. Journal of Nonlinear Sciences and Applications, 10(12):6219C6228, 2017.
10. Pro S.S., Kim T., RIM S.H.: Degenerate Daehee Numbers of the Third Kind. Bulletin of the Malaysian Mathematical Society, 6(11), 2018.
11. Sun P.: Moment Representation of Bernoulli Polynomial, Euler Polynomial and Gegenbauer Polynomials. Statistics and Probability Letters, 77:748C751, 2007.
12. Sun P., Wang T.: Probabilistic Representation with Application of Stirling Numbers. Acta Mathematica Sinica Chinese Series, 41(2):281C290, 1998.
13. Wilf. H.S.: Generating Functionology. Academic Press, New York, 1990.
Published
2020-06-03
How to Cite
Hao, T., & Wuyungaowa, . (2020). Combinatorial Identities with Several Kinds of Degenerate-Daehee Sequences. Journal of Progressive Research in Mathematics, 16(2), 2942-2954. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/1865
Section
Articles