JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE VALUES OF AN EULER SUM AT THE NEGATIVE INTEGERS AND A RELATION TO A CERTAIN CONVOLUTION OF BERNOULLI NUMBERS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE VALUES OF AN EULER SUM AT THE NEGATIVE INTEGERS AND A RELATION TO A CERTAIN CONVOLUTION OF BERNOULLI NUMBERS
Boyadzhiev, Khristo N.; Gadiyar, H. Gopalkrishna; Padma, R.;
  PDF(new window)
 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.
 Keywords
Dirichlet series;Euler sum;Bernoulli number;Hankel contour integration;
 Language
English
 Cited by
1.
Ramanujan summation and the exponential generating function $\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\zeta^{\prime}(-k)$, The Ramanujan Journal, 2010, 21, 1, 99  crossref(new windwow)
2.
Nonlinear Euler sums, Pacific Journal of Mathematics, 2014, 272, 1, 201  crossref(new windwow)
 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 crossref(new window)

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 crossref(new window)

3.
K. N. Boyadzhiev, Consecutive evaluation of Euler sums, Int. J. Math. Math. Sci. 29 (2002), no. 9, 555-561 crossref(new window)

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 crossref(new window)

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 crossref(new window)

7.
H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, 2001