본문 바로가기
KERD
논문KCI 등재

q-analogues of some results for the Apostol-Euler polynomials

2

조회

0

다운로드

7

인용

0

참고문헌

키워드

주제분류수학

초록

We investigate some bacic properties and the generating functions of q-Apostol-Euler polynomials of higher order. Several interesting relationships between the q-Apostol-Euler polynomials and q-Hurwitz-Lerch Zeta function are obtained. We also try to give some conjectures concerning the multiplication formulas of q-Apostol-Euler polynomials of higher order.

Abstract

We investigate some bacic properties and the generating functions of q-Apostol-Euler polynomials of higher order. Several interesting relationships between the q-Apostol-Euler polynomials and q-Hurwitz-Lerch Zeta function are obtained. We also try to give some conjectures concerning the multiplication formulas of q-Apostol-Euler polynomials of higher order.

참고문헌 (34)

  1. M. Cenkci, "Some results on q-analogue of the Lerch zeta function", Adv. Stud. Contemp. Math., 12, pp.213~223 (2006)
  2. M. Cenkci, "Congruences for generalized q-Bernoulli polynomials", J. Inequal. Appl., pp.19~ (2008)
  3. J. Choi, "Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz Zeta function", Appl. Math. Comput., 199, pp.723~737 (2008)
  4. J. Choi, "Carlitz's q-Bernoulli and q-Euler numbers and polynomials and a class of q-Hurwitz zeta functions", Appl. Math. Comput.
  5. A. Erdélyi, "Higher Transcendental Functions, Volume Ⅰ" (1953), McGraw-Hill
  6. G. Gasper, "Basic Hypergeometric Series (2nd edition)" (2004), Cambridge University Press
  7. S. P. Goyal, "On the generalized Riemann Zeta function and the generalized Lambert transform", Gan. ita Sandesh, 11, pp.99~108 (1997)
  8. L. Jang, "On the distribution of the q-Euler polynomials and the q-Genocchi polynomials of higher order", J. Inequal. Appl., 2008, pp.9~ (2008)
  9. T. Kim, "A note on the alternating sums of powers of consecutive q-integers", Advanced Studies in Contemporary Mathematics, 13(2), pp.159~164 (2006), 장전수학회
  10. T. Kim, "Some q-Bernoulli numbers of higher order associated with the p-adic q-integrals", Indian Pure Appl. Math., 32, pp.1565~1570 (2001)
  11. T. Kim, "A note on q-Euler numbers and Genocchi numbers", Proc. Japan Acad. Ser. A Math. Sci., 77, pp.139~141 (2001)
  12. T. Kim, "Sums of products of q-Bernoulli numbers", Arch. Math. (Basel), 76(3), pp.190~195 (2001)
  13. T. Kim, "Some formulae for the q-Bernoulli and Euler polynomial of higher order", J. Math. Anal. Appl., 273, pp.236~242 (2002)
  14. T. Kim, "On p-adic q-L-functions and sums of powers", Discrete Mathematics, 252, pp.179~187 (2002)
  15. T. Kim, "Sums of products of generalized Bernoulli numbers", Int. Math. J., 5, pp.1~7 (2004)
  16. T. Kim, "On the q-extension of Euler numbers and Genocchi numbers", J. Math. Anal. Appl, 326, pp.1458~1465 (2007)
  17. T. Kim, "On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Zp at q = −1", J. Math. Anal. Appl, 331, pp.779~792 (2007)
  18. 김태균, "On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions", 대한수학회지, 45(2), pp.435~453 (2008), 대한수학회
  19. T. Kim, "On the multiple q-Genocchi and Euler numbers", Russian Journal of Mathematical Physics, 15(4), pp.481~486 (2008)
  20. T. Kim, "Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on Zp", Russian Journal of Mathematical Physics, 17(1) (2010)
  21. Y.-H. Kim, "On the q-Extension of Apostol-Euler Numbers and Polynomials", Abst. Appl. Anal., 2008, pp.10~ (2008)
  22. S.-D. Lin, "Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations", Appl. Math. Comput., 154, pp.725~733 (2004)
  23. Q.-M. Luo, "Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials", J. Math. Anal. Appl., 308, pp.290~302 (2005)
  24. Q.-M. Luo, "Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions", Taiwanese J. Math., 10, pp.917~925 (2006)
  25. Q.-M. Luo, "The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order", Integral Transform. Spec. Funct., 20, pp.377~391 (2009)
  26. Q.-M. Luo, "q-extensions for the Apostol-Genocchi polynomials", Gen. Math., 17(2), pp.113~125 (2009)
  27. Q.-M. Luo, "q-Extensions of some relationships between the Bernoulli and Euler polynomials", Taiwanese J. Math.
  28. W. Magnus, "Formulas and Theorems for the Special Functions of Mathematical Physics, Third Enlarged Edition" (1966), Springer-Verlag
  29. H. Ozden, "Multivariate interpolation functions of higher-order q-Euler numbers and their applications", Appl. Anal. (2008)
  30. H. Ozden, "Remarks on sum of products of (h; q)-twisted Euler polynomials and numbers", J. Inequal. Appl., 2008, pp.8~ (2008)
  31. H. Ozden, "A new extension of q-Euler numbers and polynomials related to their interpolation functions", Appl. Math. Letters, 21, pp.934~939 (2008)
  32. Y. Simsek, "New approach to the complete sum of products of the twisted (h; q)-Bernoulli numbers and polynomials", J. Nonlinear Math. Phys., 14, pp.44~56 (2007)
  33. Y. Simsek, "Twisted (h, q)-Bernoulli numbers and polynomials related to twisted (h, q)-zeta function and L-function", J. Math. Anal. Appl., 324, pp.790~804 (2006)
  34. H. M. Srivastava, "q-Bernoulli numbers and polynomials associated with multiple q-Zeta functions and basic L-series", Russian J. Math. Phys., 12, pp.241~268 (2005)

관련 논문AI추천

이 간행물의 다른 논문 (13건)