Skip to main content
Log in

Some identities on the q-Euler polynomials of higher order and q-stirling numbers by the fermionic p-adic integral on ℤ p

  • Published:
Russian Journal of Mathematical Physics Aims and scope Submit manuscript

Abstract

A systemic study of some families of q-Euler numbers and families of polynomials of Nörlund type is presented by using the multivariate fermionic p-adic integral on ℤ p . The study of these higher-order q-Euler numbers and polynomials yields an interesting q-analog of identities for Stirling numbers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. I. N. Cangul, H. Ozden, and Y. Simsek, “A New Approach to q-Genocchi Numbers and Their Interpolation Functions,” Nonlinear Anal. (in press; doi:10.1016/j.na.2008.11.040).

  2. L. Comtet, Advanced Combinatorics (D. Reidel, Dordrecht, 1974).

    MATH  Google Scholar 

  3. E. Y. Deeba and D. M. Rodriguez, “Stirling’s Series and Bernoulli Numbers,” Amer. Math. Monthly 98, 423–426 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Cenkci, M. Can, and V. Kurt, “p-Adic Interpolation Functions and Kummer-Type Congruences for q-Twisted Euler Numbers,” Adv. Stud. Contemp. Math. 9, 203–216 (2004).

    MATH  MathSciNet  Google Scholar 

  5. T. Kim, S.-D. Kim, and D.-W. Park, “On Uniform Differentiability and q-Mahler Expansions,” Adv. Stud. Contemp. Math. 4, 35–41 (2001).

    MATH  Google Scholar 

  6. T. Kim, “The Modified q-Euler Numbers and Polynomials,” Adv. Stud. Contemp. Math. 16, 161–170 (2008).

    MATH  Google Scholar 

  7. T. Kim, “Euler Numbers and Polynomials Associated with Zeta Functions,” Abstr. Appl. Anal. (2008), 11 pages (Article ID 581582).

  8. K. Shiratani and S. Yamamoto, “On a p-Adic Interpolation Function for the Euler Numbers and Its Derivatives,” Mem. Fac. Sci. Kyushu Univ. Ser. A 39, 113–125 (1) (1985).

    MATH  MathSciNet  Google Scholar 

  9. T. Kim, “Note on the Euler q-Zeta Functions,” J. Number Theory (in press, doi:10.1016/j.jnt, 2009).

  10. T. Kim, “q-Volkenborn Integration,” Russ. J. Math. Phys. 9(2), 288–299 (2002).

    MATH  MathSciNet  Google Scholar 

  11. T. Kim, “A Note on p-Adic q-Integral on Zp Associated with q-Euler Numbers,” Adv. Stud. Contemp. Math. 15(2), 133–138 (2007).

    MATH  MathSciNet  Google Scholar 

  12. T. Kim, “On p-Adic Interpolating Function for q-Euler Numbers and Its Derivatives,” J. Math. Anal. Appl. 339(1), 598–608 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  13. T. Kim, “q-Extension of the Euler Formula and Trigonometric Functions,” Russ. J. Math. Phys. 14(3), 275–278 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  14. 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(2), 186–196 (2005).

    MATH  MathSciNet  Google Scholar 

  15. T. Kim, “Non-Archimedean q-Integrals Associated with Multiple Changhee q-Bernoulli Polynomials,” Russ. J. Math. Phys. 10(1), 91–98 (2003).

    MATH  MathSciNet  ADS  Google Scholar 

  16. T. Kim, “q-Euler Numbers and Polynomials Associated with p-Adic q-Integrals,” J. Nonlinear Math. Phys. 14(1), 15–27 (2007).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. H. Ozden, Y. Simsek, S.-H. Rim, and I. N. Cangul, “A Note on p-Adic q-Euler Measure,” Adv. Stud. Contemp. Math. 14(2), 233–239 (2007).

    MathSciNet  Google Scholar 

  18. M. Schork, “Ward’s “Calculus of Sequences,” q-Calculus and the Limit q → −1,” Adv. Stud. Contemp. Math. 13(2), 131–141 (2006).

    MATH  MathSciNet  Google Scholar 

  19. M. Schork, “Combinatorial Aspects of Normal Ordering and Its Connection to q-Calculus,” Adv. Stud. Contemp. Math. 15(1), 49–57 (2007).

    MATH  MathSciNet  Google Scholar 

  20. Y. Simsek, “On p-Adic Twisted q-L-Functions Related to Generalized Twisted Bernoulli Numbers,” Russ. J. Math. Phys. 13(3), 340–348 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  21. Y. Simsek, “Theorems on Twisted L-Function and Twisted Bernoulli Numbers,” Adv. Stud. Contemp. Math. 11(2), 205–218 (2005).

    MATH  MathSciNet  Google Scholar 

  22. Y. Simsek, “q-Dedekind Type Sums Related to q-Zeta Function and Basic L-Series,” J. Math. Anal. Appl. 318(1), 333–351 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  23. H. J. H. Tuenter, “A Symmetry of Power Sum Polynomials and Bernoulli,” Amer. Math. Monthly 108(3), 258–261 (2001).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. Kim.

Additional information

The present research has been conducted by the research Grant of Kwangwoon University in 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, T. Some identities on the q-Euler polynomials of higher order and q-stirling numbers by the fermionic p-adic integral on ℤ p . Russ. J. Math. Phys. 16, 484–491 (2009). https://doi.org/10.1134/S1061920809040037

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061920809040037

Keywords

Navigation