Acknowledgement
The researcher wishes to extend his sincere gratitude to the Deanship of Scientific Research at the Islamic University of Madinah for the support provided to the Post-Publishing Program 1.
References
- L. Carlitz, A note on Bernoulli and Euler polynomials of the second kind, Scripta Math. 25 (1961), 323-330.
- L. Comtet, Advanced Combinatorics, Reidel, Dordrecht, 1974.
- D.V. Dolgy, T. Kim, B. Lee and S.-H. Lee, Some new identities on the twisted Bernoulli and Euler polynomials, J. Comput. Anal. Appl. 14 (2013), 441-451.
- B.S. El-Desouky, The multiparameter non-central Stirling numbers, Fibonacci Quart. 32 (1994), 218-225.
- B.S. El-Desouky and R.S. Gomaa, Multiparameter Poly-Cauchy and Poly-Bernoulli numbers and polynomials, Int. J. Math. Anal. 9 (2015), 2619-2633. https://doi.org/10.12988/ijma.2015.58205
- B.S. El-Desouky and A. Mustafa, New results and matrix representation for Daehee and Bernoulli numbers and polynomials, Appl. Math. Sci. 9 (2015), 3593-3610.
- B.S. El-Desouky and A. Mustafa, New results on higher-order Daehee and Bernoulli numbers and polynomials, Adv. Diff. Eqs. 2016:32 (2016), DOI 10.1186/s13662-016-0764-z.
- D.S. Kim, T. Kim, S.-H. Lee and J-J. Seo, Higher-order Daehee numbers and polynomials, Int. J. Math. Anal. 8 (2014), 273-283. https://doi.org/10.12988/ijma.2014.4118
- D.S. Kim, T. Kim, S.-H. Lee and J-J. Seo, A note on the lambda Daehee polynomials, Int. J. Math. Anal. 7 (2013), 306-3080.
- D.S. Kim, T. Kim, S.-H. Lee and J-J. Seo, A note on twisted λ- Daehee polynomials, Appl. Math. Sci. 7 (2013), 7005-7014.
- D.S. Kim and T. Kim, Daehee numbers and polynomials, Appl. Math. Sci. 7 (2013), 5969-5976.
- T. Kim and Y. Simsek, Analytic continuation of the multiple Daehee q-l-functions associated with Daehee numbers, Russ. J. Math. Phys. 15 (2008), 58-65. https://doi.org/10.1134/S106192080801007X
- N. Kimura, On universal higher order Bernoulli numbers and polynomials, Report of the Research Institute of Industrial Technology, Nihon University, 70 (2003), ISSN 0386-1678.
- G.-D. Liu and H.M. Srivastava, Explicit formulas for the Norlund polynomials Bn(x) and bn(x), Comput. Math. Appl. 51 (2006), 1377-1384. https://doi.org/10.1016/j.camwa.2006.02.003
- H. Ozden, N. Cangul and Y. Simsek, Remarks on q-Bernoulli numbers associated with Daehee numbers, Adv, Stud. Contemp. Math. 18 (2009), 41-48.
- W. Wang, Generalized higher order Bernoulli number pairs and generalized Stirling number pairs, J. Math. Anal. Appl. 364 (2010), 255-274. https://doi.org/10.1016/j.jmaa.2009.10.023