General order Euler sums with multiple argument

We provide an explicit analytical representation for Euler type sums of harmonic numbers with multiple arguments. We also explore the representation of integrals with logarithmic and hypergeometric integrand in terms of the polygamma function and other special functions. The integrals in question will be associated with harmonic numbers of positive terms. A few examples of integrals will be given an identity in terms of some special functions including the Riemann zeta function.