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Some closed formulas for generalizations of Bernoulli and Euler numbers and polynomials

Z. Zhang|H. Yang
장전수학회 (Jangjeon Mathematical Society)|2008.12|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제11권 제2호|pp. 191-198|DOI 10.17777/pjms.2008.11.2.008

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키워드

Euler polynomialsBernoulli numbersEuler numbersBernoulli polynomialsgeneralized Bernoulli numbers and polynomialsgeneralized Euler numbers and polynomials
주제분류수학

초록

The purpose of this paper is to give some recurrence relations and closed formulas of generalized Bernoulli-Euler numbers and polynomials.

Abstract

The purpose of this paper is to give some recurrence relations and closed formulas of generalized Bernoulli-Euler numbers and polynomials.

참고문헌 (17)

  1. 2008, "Euler Numbers and Polynomials Associated with Zeta Functions:11 pages. doi:10.1155", pp.Abstract and Applied Analysis Volume 2008, Article ID 581582, 581582
  2. Taekyun Kim, "The modified q-Euler numbers and polynomials", Advanced Studies in Contemporary Mathematics, 16(2), pp.161~170 (2008), 장전수학회(章田數學會)
  3. Kim, T., "T. q-Bernoulli numbers and polynomials associated with Gaussian binomial co ±-cients", Russ. J. Math. Phys, 15(1), pp.51~57 (2008)
  4. A. Erdёlyi, "Higher Transcendedtal Functions", McGraw-Hill Book Company New York Toronto and London, I (1953)
  5. H.M. Srivastava, "Series Associated with the Zeta and Related Functions" (2001), Kluwer Academic Publishers, Dordrecht, Boston and London
  6. B.-N. Guo, "Generalization of Bernoulli polynomials", Internat. j. Math. Ed. Sci. Tech, 33(3), pp.428~431 (2002)
  7. F. Qi, "Generalization of Bernoulli polynomials:http:", v4n4.html, pp.RGMIA Res. Rep. Coll, 2001[DOI]
  8. L.Comtet,Advanced Combinatories, "Reidel" (1974), Dordrecht
  9. Kim, Taekyun, "Sums of powers of consecutive q-integers", Adv. Stud. Contemp. Math. (Kyungshang), 9(1), pp.15~18 (2004)
  10. L. Carlitz, "Weighted stirling numbers of the ¯rst and second kinds I", Fibonacci Quart, 18, pp.147~162 (1980)
  11. L. Carlitz, "Weighted stirling numbers of the ¯rst and second kinds II", Fibonacci Quart, 18, pp.242~257 (1980)
  12. Q.-M. Luo, "Relationships between generalized Bernoulli numbers and polynomi- als and generalized Euler numbers and polynomials", Advanced Studies in Contemporary Mathematics, 7(1), pp.11~18 (2003)
  13. "Generalization of Euler numbers and polynomials:http:", pp.IJMMS 2003:61, 3893-3901 PII. S016117120321108X, ijmms.hindawi.com
  14. "Generalization of Bernoulli numbers and polynomials:S0161171203112070,http:", pp.IJMMS 2003:59, 3769-3776 PII, ijmms.hindawi.com.
  15. Kim, T., "q-extension of the Euler formula and trigonometric functions", Russ. J. Math. Phys, 14(3), pp.275~278 (2007)
  16. Kim, Taekyun, "On the q-analogue of gamma functions and related inequalities", Article, 6(4), pp.4~ (2005)
  17. Adiga. C., "On a q-analogue of S`aandor's funtion", JIPAM. J. Inequal. Pure Appl. Math, 4(5), pp.5~ (2003)

관련 논문AI추천

A note on Eulerian polynomials associated with Bernoulli and Euler numbers and polynomials김대산, 김영희, D. V. Dolgy, T. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제3호SOME IDENTITIES FOR THE BERNOULLI, THE EULER AND THE GENOCCHI NUMBERS AND POLYNOMIALS김태균장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제1호IDENTITIES FOR THE BERNOULLI, THE EULER AND THE GENOCCHI NUMBERS AND POLYNOMIALS김태균, Bayad장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제2호A note on the extended q-Bernoulli numbers and polynomials김영희, 김태균, 최종성장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제4호Some identities of the type 2 degenerate Bernoulli and Euler numbers권종겸, 김대산, 장관우, 정세교장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제4호ON THE GENERALIZED DEGENERATE EULER NUMBERS AND POLYNOMIALS김태균, J. J. Seo장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제4호

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