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http://dx.doi.org/10.4134/BKMS.2006.43.3.611

ON THE ALTERNATING SUMS OF POWERS OF CONSECUTIVE q-INTEGERS  

Rim, Seog-Hoon (Department of Mathematics Education, Kyungpook National University)
Kim, Tae-Kyun (Jangjon Research Institute for Mathematical Science & Physics)
Ryoo, Cheon-Seoung (Department of Mathematics, Hannam University)
Publication Information
Bulletin of the Korean Mathematical Society / v.43, no.3, 2006 , pp. 611-617 More about this Journal
Abstract
In this paper we construct q-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the q-analogue of alternating sums of powers of consecutive integers due to Euler.
Keywords
Genocchi numbers and polynomials; q-Genocchi numbers and polynomials; alternating sums of powerw;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 3
연도 인용수 순위
1 J. Faulhaber, Academia Algebrae, Darinnen die miraculosische inventiones zu den hochsten Cossen weiters continuirt und profitiert werden, Augspurg, bey Johann Ulrich Schonigs, 1631
2 Y.-Y. Shen, A note on the sums of powers of consecutive integers, Tunghai Science, 5 (2003), 101-106
3 Y. Simsek, D. Kim, T. Kim, and S. H. Rim, A note on the sums of powers of consecutive q-integers, J. Appl. Funct. Different. Equat. 1 (2006), no. 1, 10-25
4 S. O. Warnaar, On the q-analogues of the sums of cubes, Electro. J. Comb. 11 (2004), no. 1, Note 13, 2pp
5 T. Kim, Analytic continuation of multiple q-Zeta functions and their values at negative integers, Russ. J. Math. Phys. 11 (2004), no. 1, 71-76
6 T. Kim, A note on the alternating sums of powers of consecutive integers, arXiv.org:math/0508233 1 (2005), 1-4   과학기술학회마을
7 K. C. Garrett and K. Hummel, A combinatorical proof of the sum of q-cubes, Electro. J. Combin. 11 (2004), no. 1, Research Paper 9, 6pp
8 T. Kim, L.-C. Jang, and H. K. Pak, A note on q-Euler and Genocchi numbers, Proc. Japan Acad. Ser. A Math. Sci. 77 A (2001), no. 8, 139-141
9 T. Kim, Sums of powers of consecutive q-integers, Adv. Stud. Contemp. Math. (Kyungshang) 9 (2004), no. 1, 15-18
10 T. Kim, A note on exploring the sums of powers of consecutive q-integers, Advan. Stud. Contemp. Math. (Kyungshang) 11 (2005), no. 1, 137-140
11 M. Schlosser, q-analogues of the sums of consecutive integers squares, cubes, quarts, quints, Electro. J. Comb. 11 (2004), no. 1, Reserch Paper 71, 12pp
12 T. Kim, C. S. Ryoo, L. C. Jang, and S. H. Rim, Exploring the sums of powers of consecutive q-integers, Inter. J. Math. Edu. Sci. Tech. 36 (2005), no. 8, 947-956   DOI   ScienceOn
13 D. E. Knuth, Johann Faulhaber and sums of powers, Math. Comput. 61 (1993), no. 203, 277-294   DOI