Moments of log-tanh integrals

Abstract

An investigation into families of integrals containing powers of the arctanh and log functions will be undertaken in this paper. It will be shown that Euler sums play an important part in the solution of these integrals. In another special case we prove that the corresponding log-tanh integral can be represented as a linear combination of the product of zeta functions and the Dirichlet eta function.

Keywords:

• Log-tanh integral
• Euler sums
• zeta functions

2010 AMS Subject Classications:

• 11M06
• 11M35
• 26B15
• 33B15
• 42A70
• 65B10

Acknowledgments

The authors are grateful to a referee(s) for pointing out some misprints and suggestions leading to a better prepared paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).