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Fourier series of higher-order Euler functions and their applications

김태균|김대산
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회보 (Bulletin of the KMS)|제55권 제1호|pp. 107-114

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참고문헌

키워드

Euler polynomialsFourier seriesEuler functions
주제분류수학

초록

In this paper, we give some identities for the higher-order Euler functions arising from the Fourier series of them. In addition, we investigate some formulae related to Bernoulli functions which are derived from our identities.

Abstract

In this paper, we give some identities for the higher-order Euler functions arising from the Fourier series of them. In addition, we investigate some formulae related to Bernoulli functions which are derived from our identities.

참고문헌 (20)

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  7. 김대산, "Nonlinear differential equation for Korobov numbers", Advanced Studies in Contemporary Mathematics, 26(4), pp.733~740 (2016), 장전수학회
  8. D. S. Kim, "Barnes-type Boole polynomials", Contrib. Discrete Math., 11(1), pp.7~15 (2016)
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  10. T. Kim, "Euler numbers and polynomials associated with zeta functions", Abstr. Apol. Anal., 2008, pp.11~ (2008)
  11. 김태균, "SOME IDENTITIES FOR THE BERNOULLI, THE EULER AND THE GENOCCHI NUMBERS AND POLYNOMIALS", Advanced Studies in Contemporary Mathematics, 20(1), pp.23~28 (2010), 장전수학회
  12. 김태균, "A note on the values of Euler zeta functions at positive integers", Advanced Studies in Contemporary Mathematics, 22(1), pp.27~34 (2012), 장전수학회
  13. T. Kim, "On <TEX>$\lambda$<", TEX>-Bell Polynomials associated with umbral calculus, 2017, pp.24(1), 1~10
  14. T. Kim, "A note on nonlinear Changhee differential equations", Russ. J. Math. Phys., 23(1), pp.88~92 (2016)[DOI]
  15. T. Kim, "Identities involving degenerate Euler numbers and polynomials arising from non-linear differential equations", J. Nonlinear Sci. Appl., 9(5), pp.2086~2098 (2016)[DOI]
  16. H. I. Kwon, "Some new identities of symmetry for modified degenerate Euler polynomials", Proc. Jangjeon Math. Soc., 19(2), pp.237~242 (2016)
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  19. L. C. Washington, "Introduction to Cyclotomic Fields, Second edition;Graduate Text in Mathematics 83" (1997), Springer-Verlag
  20. A. Sharma, "q-Bernoulli and Euler numbers of higher order", Duke Math. J., 25, pp.343~353 (1958)[DOI]

관련 논문AI추천

FOURIER SERIES OF FUNCTIONS RELATED TO TWO VARIABLE HIGHER-ORDER FUBINI POLYNOMIALS권종겸, 김대산, 김태균, 장관우, Dmitry V. Dolgy장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제4호FOURIER SERIES OF FUNCTIONS RELATED TO BERNOULLI POLYNOMIALS김대산, 김태균, 장관우, Toufik Mansour장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호FOURIER SERIES OF SUMS OF PRODUCTS OF HIGHER-ORDER GENOCCHI FUNCTIONS권종겸, 권혁인, 김대산, 김태균장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제2호Note on the Euler numbers and polynomialsT. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제17권 제2호SUMS OF PRODUCTS OF TWO VARIABLE HIGHER-ORDER FUBINI FUNCTIONS ARISING FROM FOURIER SERIES김대산, 김태균, 장관우, 장이채, Dmitry V. Dolgy장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제3호Special values and integral representations for the Hurwitz-type Euler zeta functions김대열, 김민수, Su Hu대한수학회 · 대한수학회지2018 · 제55권 제1호

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