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Note on the Euler numbers and polynomials

T. Kim
장전수학회 (Jangjeon Mathematical Society)|2008.10|Advanced Studies in Contemporary Mathematics|제17권 제2호|pp. 131-136

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참고문헌

키워드

Euler numbersFourier transforminfinite seriesEuler function.
주제분류수학

초록

In this paper we investigate the properties of the Euler functions. By using the Fourier transform for the Euler function, we derive the interesting formula related to the infinite series. Finally we give some interesting identities between the Euler numbers and the second kind stirling numbers.

Abstract

In this paper we investigate the properties of the Euler functions. By using the Fourier transform for the Euler function, we derive the interesting formula related to the infinite series. Finally we give some interesting identities between the Euler numbers and the second kind stirling numbers.

참고문헌 (30)

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  3. M. Cenkci, "Some results on q-analogue of the Lerch zeta function", Adv. Stud. Contemp. Math, 12, pp.213~223 (2006)
  4. M. Cenkci, "p-adic interpolation functions and Kummer-type congruences for q-twisted and q-generalized twisted Euler numbers", Adv. Stud. Contemp. Math, 9, pp.203~216 (2004)
  5. T. Kim, "Euler Numbers and Polynomials Associated with Zeta Functions", Abstract and Applied Analysis, 2008, pp.11~ (2008)
  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, "q-Volkenborn Integration", Russian J. Math. Phys, 9, pp.288~299 (2002)
  8. T. Kim, "q-Bernoulli numbers and polynomials associated with Gaussian binomial coe cients", Rus- sian J. Math. Phys, 15, pp.51~57 (2008)
  9. T. Kim, "q-extension of the Euler formula and trigonometric functions", Russian J. Math. Phys, 14, pp.275~278 (2007)
  10. T. Kim, "Extended q-Euler numbers and polynomials associated with fermionic p-adic q-integral on Zp", Russian J. Math. Phys, 14, pp.160~163 (2007)
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  18. Taekyun Kim, "A note on p-adic invariant integral in the rings of p -adic integers", Advanced Studies in Contemporary Mathematics, 13(1), pp.95~99 (2006), 장전수학회(章田數學會)
  19. Y. Simsek, "On interpolation functions of the twisted generalized Frobenius-Euler numbers", Advanced Studies in Contemporary Mathematics, 15(2), pp.187~194 (2007), 장전수학회(章田數學會)
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  21. H. Ozden, "Euler polynomials associated with p-adic q-Euler measure", General Mathematics, 15, pp.24~37 (2007)
  22. Yilmaz Simsek, "Generating functions of the twisted Bernoulli numbers and polynomials associated with their interpolation functions", Advanced Studies in Contemporary Mathematics, 16(2), pp.251~278 (2008), 장전수학회(章田數學會)
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  27. Y. Simsek, "Remarks on Dedekind eta function, theta functions and Eisenstein series under the Hecke operators", Advanced Studies in Contemporary Mathematics, 10, pp.15~24 (2005)
  28. Y. Simsek, "Transformation of four Titchmarsh-type in¯nite integrals and generalized Dedekind sums associated with Lambert series", Advanced Studies in Contemporary Mathematics, 9, pp.195~202 (2004)
  29. Y. Simsek, "On p-adic twisted q-L-functions related to generalized twisted Bernoulli numbers", Russian J. Math. Phys, 13, pp.340~348 (2006)
  30. T. Kim, "q-Riemann zeta function", International Journal of Mathematics and Mathematical Sciences, 2004(12), pp.509~605 (2004)

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