Symmetry of power sum and twisted Bernoulli polynomials

Advanced Studies in Contemporary Mathematics (Kyungshang)

Volumn 18, Issue 2, 2009, Pages 127-133

  Kim, Young Hee ^a   Hwang, Kyung Won ^b  

^a Kwangwoon University   (South Korea)

^b Kookmin University   (South Korea)

Author keywords

Bernoulli numbers and polynomials; P adic invariant integral; Symmetry; Twisted Bernoulli numbers and polynomials

Indexed keywords

EID: 64749113176     PISSN: 12293067     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. L.C. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948), 987-1000.
2. M. Cenkci, Y. Simsek, V. Kurt, Further remarks on multiple p-adic q-L-function of two variables, Adv. Stud. Contemp. Math. 14 (2007), 49-68.
3. M. Cenkci, Y. Simsek, V. Kurt, Multiple two-variable p-adic q-L-function and its behavior at s = 0, Russ. J. Math. Phys. 15 (2008), no. 4, 447-459.
4. T. Ernst, Examples of a q-umbral calculus, Adv. Stud. Contemp. Math. 16 (2008), no. 1, 1-22.
5. A.S. Hegazi, M. Mansour A note on q-Bernoulli numbers and polynomials, J. Nonlinear Math. Phys. 13 (2006), 9-18.
6. T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002), 288-299.
7. T. Kim, Non-Archimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials, Russ. J. Math. Phys. 10 (2003), 91-98.
8. T. Kim, Power series and asymptotic series associated with the q-analog of the two-variable p-adic L-function, Russ. J. Math. Phys. 12 (2005), no. 2, 186-196.
9. T. Kim, Multiple p-adic L-function, Russ. J. Math. Phys. 13 (2006), no. 2, 151-157.
10. T. Kim, q-Euler numbers and polynomials associated with p-adic q-integrals, J. Nonlinear Math. Phys. 14 (2007), no. 1, 15-27.
11. p associated with q-Euler numbers, Adv. Stud. Contemp. Math. 15 (2007), 133-138.
12. T. Kim, q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients, Russ. J. Math. Phys. 15 (2008), no.1, 51-57.
13. T. Kim, On the symmetries of the q-Bernoulli polynomials, Abstr. Appl. Anal. 2008 (2008), Article ID 914367, 7 pages.
14. p for Bernoulli and Euler polynomials, Journal of Difference Equations and Applications, 14 (2008), no. 12, 1267-1277.
15. T. Kim, Note on q-Genocchi numbers and polynomials, Adv. Stud. Contemp. Math. 17 (2008), no. 1, 9-15.
16. p, Russ. J. Math. Phys. 16 (2009), no. 1, 51-54.
17. Y.-H. Kim, W. Kim, L.-C. Jang, On the q-extension of Apostol-Euler numbers and polynomials, Abstr. Appl. Anal. 2008 (2008), Article ID 296159, 10 pages.
18. B.A. Kupershmidt, Reflection symmetries of q-Bernoulli polynomials, J. Nonlinear Math. Phys. 12 (2005), 412-422.
19. H. Ozden, Y. Simsek, S.-H. Rim, I. N. Cangul, A note on p-adic q-Euler measures, Adv. Stud. Contemp. Math. 14 (2007), 233-239.
20. K.H. Park, Y.-H. Kim, On some arithmetical properties of the Genocchi numbers and polynomials, Advances in Difference Equations (2008), http://www.hindawi.com/journals/ade/aip.195049.html.
21. M. Schork, A representation of the q-fermionic commutation relations and the limit q = 1, Russ. J. Math. Phys. 12 (2005), no. 3, 394-399.
22. Y. Simsek, Theorems on twisted L-function and twisted Bernoulli numbers, Adv. Stud. Contemp. Math. 11 (2005), 205-218.
23. Y. Simsek, On p-adic twisted q-L-functions related to generalized twisted Bernoulli numbers, Russ. J. Math. Phys. 13 (2006), 340-348.
24. Y. Simsek, Complete sum of products of (h, q)-extension of the Euler polynomials and numbers, arXiv:0707.2849v1 [math.NT].
25. H.M. Srivastava, T. Kim, Y. Simsek, q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, Russ. J. Math. Phys. 12 (2005), no. 2, 241-268.
26. H.J.H. Tuenter, A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly, 108 (2001), no. 3, 258-261.