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A note on p-adic integrals associated with Bernstein and q-Bernstein polynomials

최종성
장전수학회 (Jangjeon Mathematical Society)|2011.04|Advanced Studies in Contemporary Mathematics|제21권 제2호|pp. 133-138

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참고문헌

키워드

Bernoulli numbers and polynomialsEuler numbers and polynomialsfermionic p-adic integralp-adic q-integralBernstein polynomialq-Bernstein polynomial
주제분류수학

초록

In this paper, we consider two type of p-adic integral. One is the fermionic p-adic integral for the ordinary Bernstein polynomials. The other is the p-adic q-integral for T. Kim's q-Bernstein polynomials (see [11]). From these integrations, we drive identities on the Euler numbers and q-Bernoulli numbers.

Abstract

In this paper, we consider two type of p-adic integral. One is the fermionic p-adic integral for the ordinary Bernstein polynomials. The other is the p-adic q-integral for T. Kim's q-Bernstein polynomials (see [11]). From these integrations, we drive identities on the Euler numbers and q-Bernoulli numbers.

참고문헌 (18)

  1. S. Bernstein, "Demonstration du theoreme de Weierstrass, fondee sur le calcul des probabilities", Commun. Soc. Math. Kharkow, 13, pp.1~2 (1912)
  2. L. Carlitz, "q-Bernoulli numbers and polynomials", Duke Math. J, 15, pp.987~1000 (1948)
  3. V. Gupta, "Generating function for q-Bernstein, q-Meyer-Konig-Zeller and q-Beta basis", Automation Computers Applied Mathematics, 19, pp.7~11 (2001)
  4. L.-C.Jang, "A new q-analogue of Bernoulli polynomials associated with p-adic q-integrals", Abstr. Appl. Anal, pp.6~ (2008)
  5. T. Kim, "On a q-analogue of the p-adic log gamma functions and related integrals", J. Number Theory, 76, pp.320~329 (1999)
  6. T. Kim, "q-Volkenborn integration", Russ. J. Math. Phys, 9, pp.288~299 (2002)
  7. T. Kim, "q-extension of the Euler formulae and trigonometric functions", Russ. J. Math. Phys, 14, pp.275~278 (2007)
  8. T. Kim, "q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients", Russ. J. Math. Phys, 15, pp.51~57 (2008)
  9. T. Kim, "Note on the Euler q-zeta functions", J. Number Theory, 129, pp.1798~1804 (2009)
  10. T.Kim, "Barnes-type multiple q-zeta functions and q-Euler polynomials", J. Physics A:Math. Theor, 43, pp.255201~255211 (2010)
  11. T. Kim, "A note on q-Bernstein polynomials", Russ. J. Math. Phys
  12. T.Kim, "Note on the modified q-Bernstein polynomials", Discrete Dynamics in Nature and Society 2010, pp.12~ (2010)
  13. 김태균, "SOME IDENTITIES ON THE q-BERNSTEIN POLYNOMIALS, q-STIRLING NUMBERS AND q-BERNOULLI NUMBERS", Advanced Studies in Contemporary Mathematics, 20(3), pp.335~341 (2010), 장전수학회
  14. T.Kim, "On the fermionic p-adic integral representation of Bernstein polynomials associated with Euler numbers and polynomials", arXiv:1008.5207, ~
  15. T.Kim, "On p-adic analogue of q-Bernstein polynomials and related integrals", arXiv:1009.3436, ~
  16. G. M. Phillips, "On generalized Bernstein polynomials, In Numerical Analysis", pp.263~269 (1996), World Scientific
  17. G. M. Phillips, "Bernstein polynomials based on the q-integers", Annals of Numerical Analysis, 4, pp.511~514 (1997)
  18. Y. Simsek, "A new generating function of q-Bernstein-type polynomials and their interpolation function", Abstr. Appl. Anal, pp.12~ (2010)

관련 논문AI추천

A note on q-genocchi numbers and Bernstein polynomialsT. Kim, Y. H. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제3호Some identities of the twisted q-Euler numbers and polynomials associated with q-Bernstein polynomials유천성장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제2호A STUDY ON THE q-EULER NUMBERS AND THE FERMIONIC q-INTEGRAL OF THE PRODUCT OF SEVERAL TYPE q-BERNSTEIN POLYNOMIALS ON Zp김태균장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제1호ON THE q-EULER NUMBERS AND WEIGHTED q-BERNSTEIN POLYNOMIALS김영희, 김태균, 이병제, 임석훈, 최종성장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제1호Some identities on the Bernstein and q-Genocchi polynomials김현미대한수학회 · 대한수학회보2013 · 제50권 제4호SOME IDENTITIES FOR q-BERNOULLI NUMBERS AND POLYNOMIALS ARISING FROM q-BERNSTEIN POLYNOMIALS권종겸, 김대산, 장관우, 장이채장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제4호

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