  Kronecker's first limit formula gives the polar and constant terms of the
Laurent series expansion of the Eisenstein series for SL(2,Z) at s=1. In this
article, we generalize the formula to certain maximal parabolic Eisenstein
series associated to SL(n,Z) for n greater than or equal to 2. We also show how
the generalized formula can be used to give the polar and constant terms of the
Dedekind zeta function of any number field at s=1.
