A note on degenerate type 2 Changhee polynomials and numbers
Keywords:
Degenerate type 2 Changhee polynomials; Generating functions; Stirling number of two kind; Riordan matrix method.
Abstract
In this paper, we consider the degenerate type 2 Changhee numbers and polynomials cn,λ(x) and derive some new identities involving degenerate type 2 Changhee polynomials, the type 2 Changhee polynomials, the type 2 Euler polynomials, generalized Bell numbers, the Changhee-central numbers of the second kind and Euler polynomials by using the generating fuction method and the Riordan matrix method.
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References
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[3] Sun P. Moment representation of Bernoulli polynomial, Euler polynomial and Gegenbauer polynomials[J]. Statistics and Probability Letters, 2007, 77(7):748-751.
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[6] Gaowa Ma, Wuyungaowa. Application of combinatorial enumeration methods in combinatorial sequence[D], 2012.
[7] Kim B M , Jang L C , Kim W , et al. Degenerate Changhee-Genocchi numbers and polynomials[J]. Journal of Inequalities and Applications, 2017, 2017(1):294.
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[9] Srivastava, H.M., Junesang, C.: Zeta and q-zeta functions and associated series and integrals (2015)
[10] Kim D S , Kim T . On degenerate Bell numbers and polynomials[J]. 2016.
[11] Cheon Seoung Roo, On degenerate numbers and polynomials related to the stirling numbers and the bell polynomials[J]. Global Journal of Pure and Applied Mathematics,(2016),pp.3407-
3413. Young P T . Congruences for degenerate number sequences[J]. Discrete Mathematics, 2003, 270(1-3):279-289.
[12] Mihoubi M . Bell polynomials and binomial type sequences[J]. Discrete Mathematics, 2008, 308(12):2450-2459.
[13] Kim T , San Kim D . A note on degenerate Stirling numbers of the first kind[J]. 2018.
[2] Lee-Chae Jang, C.S.Ryoo, J.J.Seo, Hyuck In Kwon. Some properties of the twisted Changhee polynomials and their zeros[J]. Applied Mathematics and Computation, 2016, 274:169-177.
[3] Sun P. Moment representation of Bernoulli polynomial, Euler polynomial and Gegenbauer polynomials[J]. Statistics and Probability Letters, 2007, 77(7):748-751.
[4] D.S. Kim, T. Kim, J. Seo, A note on Changhee polynomials and numbers, Adv. Stud. Theor. Phys. 7 (20) (2013) 933ı1003.
[5] El-Desouky B , Mustafa A . New results on higher-order Daehee and Bernoulli numbers and polynomials[J]. Advances in Difference Equations, 2016, 2016(1):32.
[6] Gaowa Ma, Wuyungaowa. Application of combinatorial enumeration methods in combinatorial sequence[D], 2012.
[7] Kim B M , Jang L C , Kim W , et al. Degenerate Changhee-Genocchi numbers and polynomials[J]. Journal of Inequalities and Applications, 2017, 2017(1):294.
[8] Sprugnoli R . Riordan arrays and combinatorial sums[M]. Elsevier Science Publishers B. V. 1994.
[9] Srivastava, H.M., Junesang, C.: Zeta and q-zeta functions and associated series and integrals (2015)
[10] Kim D S , Kim T . On degenerate Bell numbers and polynomials[J]. 2016.
[11] Cheon Seoung Roo, On degenerate numbers and polynomials related to the stirling numbers and the bell polynomials[J]. Global Journal of Pure and Applied Mathematics,(2016),pp.3407-
3413. Young P T . Congruences for degenerate number sequences[J]. Discrete Mathematics, 2003, 270(1-3):279-289.
[12] Mihoubi M . Bell polynomials and binomial type sequences[J]. Discrete Mathematics, 2008, 308(12):2450-2459.
[13] Kim T , San Kim D . A note on degenerate Stirling numbers of the first kind[J]. 2018.
Published
2019-12-10
How to Cite
Chen, S., & ., W. (2019). A note on degenerate type 2 Changhee polynomials and numbers. Journal of Progressive Research in Mathematics, 15(4), 2768-2780. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1812
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