We show how integrals over [0,1] of products of the form
log^n(x)log^m(1-x)Li_p(x)Li_q(1-x)/x can be evaluated in
terms of multiple zeta values. We also show how
integrals over [0,1] of log^n(x)log^m(1-x)x^i, i nonnegative,
can be written as rational polynomials in ordinary zeta
values and a kind of generalized binomial coefficients.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/246