Logarithmic integrals, zeta values, and tiered binomial coefficients

Michael E. Hoffman, Markus Kuba

We study logarithmic integrals of the form ${\int }_0^1{x}^i{\ln }^n(x){\ln }^m(1-x)dx$. They are expressed as a rational linear combination of certain rational numbers $(n,m{)}_i$, which we c…