JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE q-ANALOGUE OF TWISTED LERCH TYPE EULER ZETA FUNCTIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE q-ANALOGUE OF TWISTED LERCH TYPE EULER ZETA FUNCTIONS
Jang, Lee-Chae;
  PDF(new window)
 Abstract
q-Volkenborn integrals ([8]) and fermionic invariant q-integrals ([12]) are introduced by T. Kim. By using these integrals, Euler q-zeta functions are introduced by T. Kim ([18]). Then, by using the Euler q-zeta functions, S.-H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin ([25]) studied q-Genocchi zeta functions. And also Y. H. Kim, W. Kim, and C. S. Ryoo ([7]) investigated twisted q-zeta functions and their applications. In this paper, we consider the q-analogue of twisted Lerch type Euler zeta functions defined by $${\varsigma}E,q,\varepsilon(s)
 Keywords
p-adic q-integral;q-Euler number and polynomials;q-Euler zeta functions;Lerch type q-Euler zeta functions;
 Language
English
 Cited by
1.
A NOTE ON THE TWISTED LERCH TYPE EULER ZETA FUNCTIONS,;;

대한수학회보, 2013. vol.50. 2, pp.659-665 crossref(new window)
2.
A New Family of q-analogue of Genocchi Numbers and Polynomials of Higher Order,;;;

Kyungpook mathematical journal, 2014. vol.54. 1, pp.131-141 crossref(new window)
1.
A New Family of q-analogue of Genocchi Numbers and Polynomials of Higher Order, Kyungpook mathematical journal, 2014, 54, 1, 131  crossref(new windwow)
2.
A NOTE ON THE TWISTED LERCH TYPE EULER ZETA FUNCTIONS, Bulletin of the Korean Mathematical Society, 2013, 50, 2, 659  crossref(new windwow)
3.
On the Dirichlet’s type of Eulerian polynomials, Mathematical Sciences, 2014, 8, 2  crossref(new windwow)
 References
1.
L. C. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948), 987-1000. crossref(new window)

2.
M. Cenkci and M. Can, Some results on q-analogue of the Lerch zeta function, Adv. Stud. Contemp. Math. (Kyungshang) 12 (2006), no. 2, 213-223.

3.
M. Cenkci, Y. Simsek, and V. Kurt, Further remarks on multiple p-adic q-L-function of two variables, Adv. Stud. Contemp. Math. (Kyungshang) 14 (2007), no. 1, 49-68.

4.
L.-C. Jang, On a q-analogue of the p-adic generalized twisted L-functions and p-adic q-integrals, J. Korean Math. Soc. 44 (2007), no. 1, 1-10. crossref(new window)

5.
L.-C. Jang, Multiple twisted q-Euler numbers and polynomials associated with p-adic q-integrals, Adv. Difference Equ. 2008 (2008), Art. ID 738603, 11 pp.

6.
L. C. Jang, S. D. Kim, D. W. Park, and Y. S. Ro, A note on Euler number and polynomials, J. Inequal. Appl. 2006 (2006), Art. ID 34602, 5 pp.

7.
Y.-H. Kim, W. Kim, and C. S. Ryoo, On the twisted q-Euler zeta function associated with twisted q-Euler numbers, Proc. Jangjeon Math. Soc. 12 (2009), no. 1, 93-100.

8.
T. Kim, On a q-analogue of the p-adic log gamma functions and related integrals, J. Number Theory 76 (1999), no. 2, 320-329. crossref(new window)

9.
T. Kim, Some identities on the q-Euler polynomials of higher order and q-Stirling umbers by the fermionic p-adic integral on $Z_p$, Russ. J. Math. Phys. 16 (2009), no. 4, 484-491. crossref(new window)

10.
T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002), no. 3, 288-299.

11.
T. Kim, On Euler-Barnes multiple zeta functions, Russ. J. Math. Phys. 10 (2003), no. 3, 261-267.

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, Power series and asymptotic series associated with the q-analog of the two-variable p-adic L-function, Russ. J. Math. Phys. 12 (2005), no. 2, 186-196.

14.
T. Kim, Multiple p-adic L-function, Russ. J. Math. Phys. 13 (2006), no. 2, 151-157. crossref(new window)

15.
T. Kim, q-generalized Euler numbers and polynomials, Russ. J. Math. Phys. 13 (2006), no. 3, 293-298. crossref(new window)

16.
T. Kim, On the analogs of Euler numbers and polynomials associated with p-adic q-integral on $Z_p$ at q = -1, J. Math. Anal. Appl. 331 (2007), no. 2, 779-792. crossref(new window)

17.
T. Kim, p-adic interpolating function for q-Euler numbers and its derivatives, J. Math. Anal. Appl. 339 (2008), no. 1, 598-608. crossref(new window)

18.
T. Kim, Note on the Euler q-zeta functions, J. Number Theory 129 (2009), no. 7, 1798-1804. crossref(new window)

19.
H. Ozden, I. N. Cangul, and Y. Simsek, Multivariate interpolation functions of higher-order q-Euler numbers and their applications, Abstr. Appl. Anal. 2008 (2008), Art. ID 390857, 16 pp.

20.
H. Ozden, I. N. Cangul, and Y. Simsek, Remarks on sum of products of (h, q)-twisted Euler polynomials and numbers, J. Inequal. Appl. 2008 (2008), Art. ID 816129, 8 pp.

21.
H. Ozden and Y. Simsek, A new extension of q-Euler numbers and polynomials related to their interpolation functions, Appl. Math. Lett. 21 (2008), no. 9, 934-939. crossref(new window)

22.
H. Ozden, Y. Simsek, and I. N. Cangul, Euler polynomials associated with p-adic q-Euler measure, Gen. Math. 15 (2007), no. 2, 24-37.

23.
H. Ozden, Y. Simsek, S. H. Rim, and I. N. Cangul, A note on p-adic q-Euler measure, Adv. Stud. Contemp. Math. (Kyungshang) 14 (2007), no. 2, 233-239.

24.
S.-H. Rim and T. Kim, A note on p-adic Euler measure on $Z_p$, Russ. J. Math. Phys. 13 (2006), no. 3, 358-361. crossref(new window)

25.
S.-H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin, On the q-Genocchi numbers and polynomials associated with q-zeta function, Proceedings of Jangjeon Math. Soc. 12 (2009), 261-268.

26.
Y. Simsek, p-adic twisted q-L-functions related to generalized twisted Bernoulli numbers, Russ. J. Math. Phys. 13 (2006), no. 3, 340-348. crossref(new window)

27.
Y. Simsek, The behavior of the twisted p-adic (h, q)-L-functions at s = 0, J. Korean Math. Soc. 44 (2007), no. 4, 915-929. crossref(new window)

28.
Y. Simsek, On twisted q-Hurwitz zeta function and q-two-variable L-function, Appl. Math. Comput. 187 (2007), no. 1, 466-473. crossref(new window)

29.
Y. Simsek, Generating functions of the twisted Bernoulli numbers and polynomials associated with their interpolation functions, Adv. Stud. Contemp. Math. (Kyungshang) 16 (2008), no. 2, 251-278.

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), no. 1, 44-56. crossref(new window)

31.
Y. Simsek, O. Yurekli, and V. Kurt, On interpolation functions of the twisted generalized Frobenius-Euler numbers, Adv. Stud. Contemp. Math. (Kyungshang) 15 (2007), no. 2, 187-194.

32.
H. M. Srivastava, T. Kim, and Y. Simsek, q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, Russ. J. Math. Phys. 12 (2005), no. 2, 241-268.