English

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.

Keywords

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

R2 v1 2026-06-22T01:01:19.749Z