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THE VALUES OF AN EULER SUM AT THE NEGATIVE INTEGERS AND A RELATION TO A CERTAIN CONVOLUTION OF BERNOULLI NUMBERS

  • Published : 2008.05.31

Abstract

The paper deals with the values at the negative integers of a certain Dirichlet series related to the Riemann zeta function and with the expression of these values in terms of Bernoulli numbers.

References

  1. Tom. M. Apostol and T. H. Vu, Dirichlet series related to the Riemann zeta function, J. Number Theory 19 (1984), no. 1, 85-102 https://doi.org/10.1016/0022-314X(84)90094-5
  2. K. N. Boyadzhiev, Evaluation of series with Hurwitz and Lerch zeta function coefficients by using Hankel contour integrals, Appl. Math. Comput. 186 (2007), no. 2, 1559-1571 https://doi.org/10.1016/j.amc.2006.08.061
  3. K. N. Boyadzhiev, Consecutive evaluation of Euler sums, Int. J. Math. Math. Sci. 29 (2002), no. 9, 555-561 https://doi.org/10.1155/S0161171202007871
  4. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, Addison-Wesley Publishing Company, Reading, MA, 1994
  5. Y. Matsuoka, On the values of a certain Dirichlet series at rational integers, Tokyo J. Math. 5 (1982), no. 2, 399-403 https://doi.org/10.3836/tjm/1270214900
  6. H. Pan and Z.-W. Sun, New identities involving Bernoulli and Euler polynomials, J. Combin. Theory Ser. A 113 (2006), no. 1, 156-175 https://doi.org/10.1016/j.jcta.2005.07.008
  7. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, 2001

Cited by

  1. Ramanujan summation and the exponential generating function $\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\zeta^{\prime}(-k)$ vol.21, pp.1, 2010, https://doi.org/10.1007/s11139-009-9166-0
  2. Nonlinear Euler sums vol.272, pp.1, 2014, https://doi.org/10.2140/pjm.2014.272.201