Generating functions of the (h, q) extension of twisted Euler polynomials and numbers

Acta Mathematica Hungarica

Volumn 120, Issue 3, 2008, Pages 281-299

  Cangul, I N ^a   Ozden, H ^a   Simsek, Y ^b  

^a ULUDAG UNIVERSITY   (Turkey)

^b AKDENIZ UNIVERSITY   (Turkey)

Author keywords

P adic Volkenborn integral; Twisted q Euler numbers and polynomials; Zeta and l functions

Indexed keywords

EID: 48349147457     PISSN: 02365294     EISSN: 15882632     Source Type: Journal    
DOI: 10.1007/s10474-008-7139-1     Document Type: Article

References (32)

1. M. Cenkci, M. Can and V. Kurt, p-adic interpolation functions and Kummer-type congruences for q-twisted and q-generalized twisted Euler numbers, Adv. Stud. Contep. Math., 9 (2004), 203-216.
2. T. Kim, An analogue of Bernoulli numbers and their applications, Rep. Fac. Sci. Engrg. Saga Univ. Math., 22 (1994), 21-26.
3. T. Kim, q-Volkenborn integration, Russian J. Math Phys., 19 (2002), 288-299.
4. T. Kim, Non-archimedean q-integrals associated with multiple Changhee q-Bernoulli Polynomials, Russian J. Math Phys., 10 (2003), 91-98.
5. T. Kim, q-Riemann zeta function, Internat J. Math. Sci., (2003), 185-192.
6. T. Kim, p-adic q-integrals associated with the Changhee-Barnes' q-Bernoulli Polynomials, Integral Transform. Spec. Funct., 15 (2004), 415-420.
7. T. Kim, Analytic continuation of multiple q-zeta functions and their values at negative integers, Russian J. Math Phys., 11 (2004), 71-76.
8. T. Kim, A new approach to q-zeta function, Adv. Stud. Contep. Math., 11 (2005), 157-162.
9. T. Kim, On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl., 326 (2007), 1458-1465.
10. T. Kim, q-Euler numbers and polynomials associated with p-adic q-integrals, J. Nonlinear Math. Phys., 14 (2007), 15-27.
11. p at q = -1, J. Math. Anal. Appl., 331 (2007), 779-792.
12. T. Kim, On p-adic q-l-functions and sums of powers, J. Math. Anal. Appl., 329 (2007), 1472-1481.
13. p, Appl. Math. Letters, In Press, Corrected Proof, Available online 20 February 2007.
14. T. Kim, The modified q-Euler numbers and polynomials, ArXive:math.NT/0702523.
15. T. Kim and S-H. Rim, Generalized Carlitz's q-Bernoulli numbers in the p-adic number field, Adv. Stud. Contep. Math., 2 (2000), 9-19.
16. T. Kim, L. C. Jang, S-H. Rim and H. K. Pak, On the twisted q-zeta functions and q-Bernoulli polynomials, Far East J. Appl. Math., 13 (2003), 13-21.
17. T. Kim, M-S. Kim, L-C. Jang and S-H. Rim, New q-Euler numbers and polynomials associated with p-adic q-integrals, Adv. Stud. Contep. Math., 15 (2007), 140-153, arXiv:MathNT/0709.0089.
18. T. Kim, S-H. Rim and Y. Simsek, A note on the alternating sums of powers of consecutive q-integers, Adv. Stud. Contemp. Math., 13 (2006), 159-164.
19. T. Kim and S-H. Rim, On the Twisted q-Euler numbers and polynomials associated with basic q-l-functions, J. Math. Anal. (to appear).
20. N. Koblitz, A new proof of certain formulas for p-adic L-functions, Duke Math. J., 46 (1979), 455-468.
21. N. Koblitz, On Carlitz's q-Bernoulli numbers, J. Number Theory, 14 (1982), 332-339.
22. N. Koblitz, p-adic Analysis: A short course on recent work, London Math. Soc. Lecture Note Ser., 46 (1980).
23. H. Ozden, Y. Simsek, S-H. Rim and I. N. Cangul, A note on p-adic q-Euler measure, Advan. Stud. Contemp. Math., 14 (2007), 233-239.
24. H. Ozden and Y. Simsek, A new extension of q-Euler numbers and polynomials related to their interpolation functions, to appear in Applied Mathematics Letters.
25. S-H. Rim and T. Kim, New Changhee q-Euler numbers and polynomials associated with p-adic q-integral, Computers & Math. Appl., 54 (2007), 484-489, arXiv:Math:NT/0611791.
26. Y. Simsek, Theorems on twisted L-functions and twisted Bernoulli numbers, Adv. Stud. Contep. Math., 11 (2005), 205-218.
27. Y. Simsek, q-analogue of the twisted l-series and q-twisted Euler numbers, J. Number Theory, 110 (2005), 267-278.
28. Y. Simsek, Twisted (h, q)-Bernoulli numbers and polynomials related to twisted (h, q)-zeta function and L-function, J. Math. Anal. Appl., 324 (2006), 790-804.
29. Y. Simsek, On twisted q-Hurwitz zeta function and q-two-variable L-function, Appl. Math. Comput., 187 (2007), 466-473.
30. Y. Simsek, V. Kurt and D. Kim, New approach to the complete sum of products of the twisted (h, q)-Bernoulli numbers and polynomials, J. Nonlinear Math. Phys., 14 (2007), 44-56.
31. H. M. Srivastava, T. Kim and Y. Simsek, q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, Russian J. Math. Phys., 12 (2005), 241-268.
32. H. M. Srivastava and A. Pinter, Remarks on some relationships between the Bernoulli and Euler polynomials, Appl. Math. Lett., 17 (2004), 375-380.