On a degenerate \(\lambda-q\)-Daehee polynomials
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Authors
Byung Moon Kim
- Department of Mechanical System Engineering, Dongguk University, 123 Dongdae-ro, Gyungju-si, Gyeongsangbuk-do, 38066, Republic of Korea.
Sang Jo Yun
- Department of Mathematics Education, Daegu University, Gyeongsan-si, Gyeongsangbuk-do, 38453, Republic of Korea.
Jin-Woo Park
- Department of Mathematics Education, Daegu University, Gyeongsan-si, Gyeongsangbuk-do, 38453, Republic of Korea.
Abstract
Daehee numbers and polynomials are introduced by Kim [T. Kim, Integral Transforms Spec. Funct.,
13 (2002), 65-69] and [D. S. Kim, T. Kim, Appl. Math. Sci. (Ruse), 7 (2013), 5969-5976], and those
polynomials and numbers are generalized by many researchers. In this paper, we make an attempt to
degenerate \(\lambda-q\)-Daehee polynomials, and derive some new and interesting identities and properties of those
polynomials and numbers.
Share and Cite
ISRP Style
Byung Moon Kim, Sang Jo Yun, Jin-Woo Park, On a degenerate \(\lambda-q\)-Daehee polynomials, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4607--4616
AMA Style
Kim Byung Moon, Yun Sang Jo, Park Jin-Woo, On a degenerate \(\lambda-q\)-Daehee polynomials. J. Nonlinear Sci. Appl. (2016); 9(6):4607--4616
Chicago/Turabian Style
Kim, Byung Moon, Yun, Sang Jo, Park, Jin-Woo. "On a degenerate \(\lambda-q\)-Daehee polynomials." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4607--4616
Keywords
- \(\lambda\)-Daehee polynomials
- \(q\)-Daehee polynomials
- degenerate \(\lambda-q\)-Daehee polynomials.
MSC
References
-
[1]
L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math., 15 (1979), 51--88
-
[2]
Y. K. Cho, T. Kim, T. Mansour, S. H. Rim, Higher-order q-Daehee polynomials, J. Comput. Anal. Appl., 19 (2015), 167--173
-
[3]
L. Comtet, Advanced Combinatorics, Reidel Publishing Co., Dordrecht (1974)
-
[4]
B. S . El-Desouky, A. Mustafa, New results on higher-order Daehee and Bernoulli numbers and polynomials, Adv. Difference Equ., 2016 (2016), 21 pages
-
[5]
T. Kim, On q-analogye of the p-adic log gamma functions and related integral, J. Number Theory, 76 (1999), 320--329
-
[6]
T. Kim, q-Volkenborn integration, Russ. J. Math. Phys., 9 (2002), 288--299
-
[7]
T. Kim, An invariant p-adic integral associated with Daehee numbers, Integral Transforms Spec. Funct., 13 (2002), 65--69
-
[8]
D. S. Kim, T. Kim, Daehee numbers and polynomials, Appl. Math. Sci. (Ruse), 7 (2013), 5969--5976
-
[9]
T. Kim, D. S. Kim, A Note on Nonlinear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 88--92
-
[10]
D. S. Kim, T. Kim, H. I. Kwon, T. Mansour, Powers under umbral composition and degeneration for Sheffer sequences, Adv. Difference Equ., 2016 (2016), 11 pages
-
[11]
D. S. Kim, T. Kim, S. H. Lee, J. J. Seo, A note on the lambda-Daehee polynomials, Int. J. Math. Anal. (Ruse), 7 (2013), 3069--3080
-
[12]
T. Kim, Y. Simsek, Analytic continuation of the multiple Daehee q-l-functions associated with Daehee numbers, Russ. J. Math. Phys., 15 (2008), 58--65
-
[13]
H. Ozden, I. N. Cangul, Y. Simsek, Remarks on q -Bernoulli numbers associated with Daehee numbers, Adv. Stud. Contemp. Math. (Kyungshang), 18 (2009), 41--48
-
[14]
J. W. Park, On the q-analogue of \(\lambda\)-Daehee polynomials, J. Comput. Anal. Appl., 19 (2015), 966--974
-
[15]
J. W. Park, S. H. Rim, J. Kwon, The twisted Daehee numbers and polynomials, Adv. Difference Equ., 2014 (2014), 9 pages
-
[16]
S. Roman, The umbral calculus, Springer, New York (2005)
-
[17]
J. J. Seo, S. H. Rim, T. Kim, S. H. Lee, Sums products of generalized Daehee numbers, Proc. Jangjeon Math. Soc., 17 (2014), 1--9
-
[18]
Y. Simsek, S. H. Rim, L. C. Jang, D. J. Kang, J. J. Seo, A note on q-Daehee sums, J. Anal. Comput., 1 (2005), 151--160