On Gould-Hopper based fully degenerate Type2 poly-Bernoulli polynomials with a \(q\)-parameter
Authors
E. Negiz
- Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkiye.
M. Acikgoz
- Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkiye.
U. Duran
- Department of Basic Sciences of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, TR-31200, Hatay, Turkiye.
Abstract
In this paper, the Gould-Hopper based fully degenerate type2 poly-Stirling
polynomials of the first kind with a \(q\) parameter are considered and some
of their diverse identities and properties are investigated. Then, the
Gould-Hopper based fully degenerate type2 poly-Bernoulli polynomials with a
\(q\) parameter are introduced and some of their properties are analyzed and
derived. Furthermore, several formulas and relations covering implicit
summation formulas, recurrence relations and symmetric property are attained.
Share and Cite
ISRP Style
E. Negiz, M. Acikgoz, U. Duran, On Gould-Hopper based fully degenerate Type2 poly-Bernoulli polynomials with a \(q\)-parameter, Journal of Nonlinear Sciences and Applications, 16 (2023), no. 1, 18--29
AMA Style
Negiz E., Acikgoz M., Duran U., On Gould-Hopper based fully degenerate Type2 poly-Bernoulli polynomials with a \(q\)-parameter. J. Nonlinear Sci. Appl. (2023); 16(1):18--29
Chicago/Turabian Style
Negiz, E., Acikgoz, M., Duran, U.. "On Gould-Hopper based fully degenerate Type2 poly-Bernoulli polynomials with a \(q\)-parameter." Journal of Nonlinear Sciences and Applications, 16, no. 1 (2023): 18--29
Keywords
- Gould-Hopper polynomials
- Bernoulli polynomials
- poly-Bernoulli polynomials
- degenerate Bernoulli function
- Stirling numbers of the first kind
MSC
References
-
[1]
A. Bayad, Y. Hamahata, Polylogarithms and poly-Bernoulli polynomials, Kyushu J. Math., 65 (2011), 15–24
-
[2]
M. Cenkci, T. Komatsu, Poly-Bernoulli numbers and polynomials with a q parameter, J. Number Theory, 152 (2015), 38–54
-
[3]
Some discrete d-orthogonal polynomial sets, Y. B. Cheikh, A. Zaghouani, J. Comput. Appl. Math., 156 (2003), 253–263
-
[4]
G. Dattoli, S. Lorenzutta, C. Cesarano, Finite sums and generalized forms of Bernoulli polynomials, Rend. Mat. Appl., 19 (1999), 385–391
-
[5]
U. Duran, M. Acikgoz, Generalized Gould-Hopper based fully degenerate central Bell polynomials, Turkish J. Anal. Number Theory, 7 (2019), 124–134
-
[6]
U. Duran, M. Acikgoz, S. Araci, Hermite based poly-Bernoulli polynomials with a q-parameter, Adv. Stud. Contemp. Math., 28 (2018), 285–296
-
[7]
U. Duran, P. N. Sadjang, On Gould-Hopper-based fully degenerate poly-Bernoulli polynomials with a q-parameter, Mathematics, 7 (2019), 1–14
-
[8]
W. A. Khan, A note on degenerate Hermite poly-Bernoulli numbers and polynomials, J. Class. Anal., 8 (2016), 65–76
-
[9]
W. A. Khan, N. U. Khan, S. Zia, A note on Hermite poly-Bernoulli numbers and polynomials of the second kind, Turkish J. Anal. Number Theory, 3 (2015), 120–125
-
[10]
T. Kim, D. S. Kim, H. Y. Kim, L.-C. Jang, Degenerate Poly-Bernoulli numbers and polynomials, Informatica, 31 (2020), 2–8
-
[11]
D. S. Kim, T. K. Kim, T. Mansour, J.-J. Seo, Fully degenerate poly-Bernoulli polynomials with a q parameter, Filomat, 30 (2016), 1029–1035
-
[12]
T. Kim, D. S. Kim, J.-J. Seo, Fully degenerate poly-Bernoulli numbers and polynomials, Open Math., 14 (2016), 545–556
-
[13]
B. Kurt, Y. Simsek, On the Hermite based Genocchi polynomials, Adv. Stud. Contemp. Math., 23 (2013), 13–17
-
[14]
M. A. O¨ zarslan, Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials, Adv. Differ. Equ., 2013 (2013), 13 pages
-
[15]
M. A. Pathan, W. A. Khan, Some implicit summation formulas and symmetric identities for the generalized Hermite- Bernoulli polynomials, Mediterr. J. Math., 12 (2015), 679–695
-
[16]
H. M. Srivastava, M. Garg, S. Choudhary, A new generalization of the Bernoulli and related polynomials, Russ. J. Math. Phys., 17 (2010), 251–261