Evaluation of integrals with hypergeometric and logarithmic functions

Abstract

We provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions. The integrals in question will be associated with both alternating harmonic numbers and harmonic numbers with positive terms. A few examples of integrals will be given an identity in terms of some special functions including the Riemann zeta function. In general none of these integrals can be solved by any currently available mathematical package.

Keywords

• polylogarithm function
• integral representation
• lerch transcendent function
• logarithmic integral
• riemann zeta function
• 05a10
• 05a19
• 33c20
• 11b65
• 11b83
• 11m06