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NOTE ON CARLITZ’S TYPE q-EULER NUMBERS AND POLYNOMIALS

김영희|김태균|이병제
장전수학회 (Jangjeon Mathematical Society)|2010.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제13권 제2호|pp. 149-155|DOI 10.17777/pjms.2010.13.2.004

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참고문헌

키워드

q-Euler numbers and polynomialszeta functionLaurent seriesCauchy residue theorem
주제분류수학

초록

The purpose of this paper is to consider Carlitz’s type q-Euler numbers and polynomials. We present new generating functions for Carlitz’s type q-Euler numbers and polynomials. We have the recurrence formula for these q-Euler numbers and polynomials. We obtain a distribution relation for the q-Euler polynomials, and have some identities for the q-Euler numbers and polynomials.

Abstract

The purpose of this paper is to consider Carlitz’s type q-Euler numbers and polynomials. We present new generating functions for Carlitz’s type q-Euler numbers and polynomials. We have the recurrence formula for these q-Euler numbers and polynomials. We obtain a distribution relation for the q-Euler polynomials, and have some identities for the q-Euler numbers and polynomials.

참고문헌 (17)

  1. L. Carlitz, "q-Bernoulli numbers and polynomials", Duke Mathematical Journal, 15, pp.987~1000 (1948)
  2. L. Carlitz, "q-Bernoulli Eulerian numbers", Transactions of the American Mathematical Society, 76, pp.332~350 (1954)
  3. M. Cenkci, "Some results on q-analogue of the Lerch Zeta function", Advanced Studies in Contemporary Mathematics, 12, pp.213~223 (2006)
  4. T. Kim, "On a q-analogue of the p-adic log gamma functions and related integrals", Journal of Number Theory, 76, pp.320~329 (1999)
  5. T. Kim, "q-generalized Euler numbers and polynomials", Russian Journal of Mathematical Physics, 13, pp.293~298 (2006)
  6. T. Kim, "q-Euler numbers and polynomials associated with p-adic q-integrals", Journal of Nonlinear Mathematical Physics, 14, pp.15~27 (2007)
  7. T. Kim, "On the q-extension of Euler and Genocchi numbers", Journal of Mathematical Analysis and Applications, 326, pp.1458~1465 (2007)
  8. Taekyun Kim, "The modified q-Euler numbers and polynomials", Advanced Studies in Contemporary Mathematics, 16(2), pp.161~170 (2008), 장전수학회
  9. T. Kim, "Note on the Euler q-zeta functions", Journal of Number Theory, 129, pp.1798~1804 (2009)
  10. 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, 16, pp.484~491 (2009)
  11. T. Kim, "New approach to q-Euler numbers and polynomials", Advances in Difference Equations, 2010, pp.9~ (2010)
  12. 김영희, "Symmetry of power sum and twisted Bernoulli polynomials", Advanced Studies in Contemporary Mathematics, 18(2), pp.127~133 (2009), 장전수학회
  13. Y.-H. Kim, "On the q-extension of Apostol-Euler numbers and polynomials", Abstract and Applied Analysis, 2008, pp.10~ (2008)
  14. 김영희, "ON THE TWISTED q-EULER ZETA FUNCTION ASSOCIATED WITH TWISTED q-EULER NUMBERS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 12(1), pp.93~100 (2009), 장전수학회
  15. H. Ozden, "Remarks on q-Bernoulli numbers associated with Daehee numbers", Advanced Studies in Contemporary Mathematics, 18(1), pp.41~48 (2009), 장전수학회
  16. H. Ozden, "A new extension of q-Euler numbers and polynomials related to their interpolation functions", Applied Mathematics Letters, 21, pp.934~939 (2008)
  17. H. Ozden, "A note on p -adic q -Euler measure", Advanced Studies in Contemporary Mathematics, 14(2), pp.233~240 (2007), 장전수학회

관련 논문AI추천

A RECURRENCE FORMULA FOR q-EULER NUMBERS OF HIGHER ORDER김영희, 김태균, 최종성장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2010 · 제13권 제3호A NEW APPROACH OF q-EULER NUMBERS AND POLYNOMIALS김영희, 김태균, 이병제, 최종성장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제1호On extended Carlitz’'s type q-Euler numbers and polynomials김영희, 김태균, 최종성장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제4호A note on the weighted q-Euler numbers and polynomials유천성장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제1호A note on the modified q-Euler numbers and polynomials with weight김영희, 김태균, 최종성장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제4호On the Modified q-Euler Numbers and Polynomials withWeak Weight 0권종겸, 박진우, 임석훈, 표성수경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제3호

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