Add to ORKGCopyright c © 2013 Huizeng Qin and Youmin Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We study the extended Euler sums and the alternating extended Euler sums and establish their explicit expressions in terms of Riemann zeta functions and Hurwitz zeta functions. Comparing with the existing results, ours are simpler and thus yield significantly better accuracy when Matlab is used for numerical calculation
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...
In response to a letter from Goldbach, Euler considered sums of the form [unable to replicate formul...
AbstractIn this paper, we consider two types of extended Euler sums:Ep,q(k)=∑n=1∞1nq∑r=1kn1rp,Tp,q(k...
Abstract. We present a simple method for evaluation of multiple Euler sums in terms of single and do...
Abstract. We present a simple method for evaluation of multiple Euler sums in terms of single and do...
Abstract. We present a simple method for evaluation of multiple Euler sums in terms of single and do...
In response to a letter from Goldbach, Euler considered sums of the form 1 X k=1 ` 1 + 1 2 m ...
Euler considered sums of the form [formula unable to be reproduced here]. Here natural generalizatio...
We describe a simple method for a consecutive evaluation of the Euler sums S(r,p), r = 1,2,... in te...
We describe a simple method for a consecutive evaluation of the Euler sums S(r,p), r = 1,2,... in te...
We describe a simple method for a consecutive evaluation of the Euler sums S(r,p), r = 1,2,... in te...
International audienceWe study three special Dirichlet series, two of them alternating, related to t...
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...
In response to a letter from Goldbach, Euler considered sums of the form [unable to replicate formul...
AbstractIn this paper, we consider two types of extended Euler sums:Ep,q(k)=∑n=1∞1nq∑r=1kn1rp,Tp,q(k...
Abstract. We present a simple method for evaluation of multiple Euler sums in terms of single and do...
Abstract. We present a simple method for evaluation of multiple Euler sums in terms of single and do...
Abstract. We present a simple method for evaluation of multiple Euler sums in terms of single and do...
In response to a letter from Goldbach, Euler considered sums of the form 1 X k=1 ` 1 + 1 2 m ...
Euler considered sums of the form [formula unable to be reproduced here]. Here natural generalizatio...
We describe a simple method for a consecutive evaluation of the Euler sums S(r,p), r = 1,2,... in te...
We describe a simple method for a consecutive evaluation of the Euler sums S(r,p), r = 1,2,... in te...
We describe a simple method for a consecutive evaluation of the Euler sums S(r,p), r = 1,2,... in te...
International audienceWe study three special Dirichlet series, two of them alternating, related to t...
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...
Euler considered sums of the form Here natural generalizations of these sums namely are investigated...