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Relations on Bernoulli and Euler polynomials related to trigonometric functions

NESLIHAN KILAR|YILMAZ SIMSEK
장전수학회 (Jangjeon Mathematical Society)|2019.04|Advanced Studies in Contemporary Mathematics|제29권 제2호|pp. 191-198

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참고문헌

키워드

Bernoulli numbers and polynomialsEuler numbers and polynomialsCosine-Bernoulli polynomialsCosine-Euler polynomialsSine-Bernoulli polynomialsSine-Euler polynomialsGen- erating functionTrigonometric function
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초록

The cosine-Euler polynomials, the sine-Euler polynomials, the cosine-Bernoulli polynomials, the sine-Bernoulli polynomials have been recently studied by Kim and Ryoo [4] and also Masjed-Jamei et al. [5]-[6] and Srivastava et al. [11]. The purpose of this paper is to derive some new identities and relations for these polynomials with aid of generating functions and trigonometric functions.

Abstract

The cosine-Euler polynomials, the sine-Euler polynomials, the cosine-Bernoulli polynomials, the sine-Bernoulli polynomials have been recently studied by Kim and Ryoo [4] and also Masjed-Jamei et al. [5]-[6] and Srivastava et al. [11]. The purpose of this paper is to derive some new identities and relations for these polynomials with aid of generating functions and trigonometric functions.

참고문헌 (11)

  1. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, "M. Abramowitz", U.S. Dept. of Com-merce, National Bureau of Standards, ~ (1972)
  2. E. Y. Deeba, "Bernoulli numbers and trigonometric functions", Int. J. Math. Educ. Sci. Technol, 21(2), pp.275~282 (1990)
  3. D. S. Kim, "Some p-adic integrals on Zp Associated with trigonometric functions", Russ. J. Math. Phys, 25(3), pp.300~308 (2018)
  4. T. Kim, "Some identities for Euler and Bernoulli polynomials and their zeros", Axioms, 7(3), pp.1~19 (2018)
  5. Mohammad Masjed-Jamei, "Symbolic computation of some power-trigonometric series", Journal of Symbolic Computation, 80, pp.273~284 (2017), Elsevier BV[DOI]
  6. M. Masjed-Jamei, "A new type of Euler polynomials and numbers", Mediterr. J. Math, 15(138), pp.1~17 (2018)
  7. Y. Simsek, "Special functions related to Dedekind-type DC-sums and their applications", Russ. J. Math. Phys, 17(4), pp.495~508 (2010)
  8. Y. Simsek, "New families of special numbers for computing negative order Euler num-bers and related numbers and polynomials", Appl. Anal. Discrete Math, 12, pp.1~35 (2018)
  9. H. M. Srivastava, "Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials", Appl. Math. Inform. Sci, 5, pp.390~444 (2011)
  10. H. M. Srivastava, "q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series", Russ. J. Math. Phys, 12, pp.241~268 (2005)
  11. H. M. Srivastava, "A parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials", Appl. Math. Inf. Sci, 12(5), pp.907~916 (2018)

관련 논문AI추천

Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomialsDan Ding, Jizhen Yang장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제1호SOME IDENTITIES FOR DEGENERATE COSINE(SINE)-EULER POLYNOMIALS정원균장전수학회 · Advanced Studies in Contemporary Mathematics2020 · 제30권 제1호Identities involving Bernoulli and Euler polynomials arising from Chebyshev polynomials김대산, D. V. Dolgy, S. H. Rim, T. Kim장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2012 · 제15권 제4호A 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 of the type 2 degenerate Bernoulli and Euler numbers권종겸, 김대산, 장관우, 정세교장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제4호THEOREMS ON APOSTOL-EULER POLYNOMIALS OF HIGHER ORDER ARISING FROM EULER BASISErdogan Sen장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제2호

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