# ON THE ALTERNATING SUMS OF POWERS OF CONSECUTIVE q-INTEGERS

• Published : 2006.08.01
• 36 10

#### 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

#### References

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. 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
3. 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
4. T. Kim, Sums of powers of consecutive q-integers, Adv. Stud. Contemp. Math. (Kyungshang) 9 (2004), no. 1, 15-18
5. 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
6. 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 https://doi.org/10.1080/00207390500138165
7. D. E. Knuth, Johann Faulhaber and sums of powers, Math. Comput. 61 (1993), no. 203, 277-294 https://doi.org/10.2307/2152953
8. 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
9. Y.-Y. Shen, A note on the sums of powers of consecutive integers, Tunghai Science, 5 (2003), 101-106
10. 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
11. S. O. Warnaar, On the q-analogues of the sums of cubes, Electro. J. Comb. 11 (2004), no. 1, Note 13, 2pp
12. 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
13. T. Kim, A note on the alternating sums of powers of consecutive integers, arXiv.org:math/0508233 1 (2005), 1-4

#### Cited by

1. Some families of Genocchi type polynomials and their interpolation functions vol.23, pp.12, 2012, https://doi.org/10.1080/10652469.2011.643627