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q-DEDEKIND-TYPE DAEHEE-CHANGHEE SUMS WITH WEIGHT α ASSOCIATED WITH MODIFIED q-EULER POLYNOMIALS WITH WEIGHT α

  • Received : 2013.11.27
  • Accepted : 2013.01.06
  • Published : 2014.02.15

Abstract

Recently, q-Dedekind-type sums related to q-Euler polynomials was studied by Kim in [T. Kim, Note on q-Dedekind-type sums related to q-Euler polynomials, Glasgow Math. J. 54 (2012), 121-125]. It is aim of this paper to consider a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order Dedekind-type sums with weight related to modified q-Euler polynomials with weight by using Kim's p-adic q-integral.

Keywords

References

  1. S. Araci, Novel Identities for the q-Genocchi numbers and polynomials, Journal of Function Spaces and Applications, 2012 (2012), Article ID 214961, 12 pages.
  2. S. Araci, M. Acikgoz, and K. H. Park, A note on the q-analogue of Kim's p-adic log gamma type functions associated with q-extension of Genocchi and Euler numbers with weight ${\alpha}$, Bull. Korean Math. Soc. 50 (2013), no. 2, 583-588. https://doi.org/10.4134/BKMS.2013.50.2.583
  3. S. Araci, D. Erdal, and J. J. Seo, A study on the fermionic p-adic q-integral representation on $\mathbb{Z}p$ associated with weighted q-Bernstein and q-Genocchi polynomials, Abstract and Applied Analysis, 2011, Article ID 649248, 10 pages.
  4. S. Araci and M. Acikgoz, A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials, Advanced Studies in Contemporary Mathematics 22 (2012), no. 3, 399-406.
  5. S. Araci, M. Acikgoz, A. Bagdasaryan, and E. Sen, The Legendre Polynomials Associated with Bernoulli, Euler, Hermite and Bernstein Polynomials, Turkish Journal of Analysis and Number Theory, no. 1 (1) (2013): 1-3. doi: 10.12691/tjant-1-1-1.
  6. T. Kim, A note on p-adic q-Dedekind sums, C. R. Acad. Bulgare Sci. 54 (2001), 37-42.
  7. T. Kim, Note on q-Dedekind-type sums related to q-Euler polynomials, Glasgow Math. J. 54 (2012), 121-125. https://doi.org/10.1017/S0017089511000450
  8. T. Kim, Note on Dedekind type DC sums, Adv. Stud. Contemp. Math. 18 (2009), 249-260.
  9. T. Kim, The modified q-Euler numbers and polynomials, Adv. Stud. Contemp. Math. 16 (2008), 161-170.
  10. T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002), 288-299.
  11. T. Kim, On p-adic interpolating function for q-Euler numbers and its derivatives, J. Math. Anal. Appl. 339 (2008), 598-608. https://doi.org/10.1016/j.jmaa.2007.07.027
  12. T. Kim, On a q-analogue of the p-adic log gamma functions and related integrals, J. Number Theory 76 (1999), 320-329. https://doi.org/10.1006/jnth.1999.2373
  13. Y. Simsek, q-Dedekind type sums related to q-zeta function and basic L-series, J. Math. Anal. Appl. 318 ( 2006), 333-351. https://doi.org/10.1016/j.jmaa.2005.06.007
  14. M. Acikgoz and Y. Simsek, On multiple interpolation function of the Norlund-type q-Euler polynomials, Abst. Appl. Anal. 2009 (2009), Article ID 382574, 14 pages.
  15. S. H. Rim and J. Jeong, A note on the Modified q-Euler Numbers and polynomials with weight ${\alpha}$, International Mathematical Forum, 6 (2011), no. 65, 3245-3250.
  16. C. S. Ryoo, A note on the weighted q-Euler numbers and polynomials, Adv. Stud. Contemp. Math. 21 (2011), 47-54.

Cited by

  1. Extended q-Dedekind-type Daehee-Changhee sums associated with extended q-Euler polynomials vol.2015, pp.1, 2015, https://doi.org/10.1186/s13662-015-0610-8