The connection between the Basel problem and a special integral
Number Theory
2015-02-10 v2 Classical Analysis and ODEs
Abstract
By using Fubini theorem or Tonelli theorem, we find that the zeta function value at 2 is equal to a special integral. Furthermore, We find that this special integral is two times of another special integral. By using this fact we obtain the relationship between Genocchi numbers and Bernoulli numbers. And get some results about Bernoulli polynomials.
Cite
@article{arxiv.1307.8278,
title = {The connection between the Basel problem and a special integral},
author = {Haifeng Xu and Jiuru Zhou},
journal= {arXiv preprint arXiv:1307.8278},
year = {2015}
}
Comments
19 pages, 0 figures