Some intriguing definite integrals
- Zacharias, Klaus
2010 Mathematics Subject Classification
- 11M99 33E99
- Riemann zeta function, polylogarithms
We calculate some definite integrals which (up to now) computer algebra systems like Maple or Mathematica are unable to evaluate. The first one is a simply looking integral involving cos and log, the others are some integrals containing polylogarithmic functions. It is shown that they can be evaluated by rational combinations of ς-functions and products of ς-functions at positive integers.