  We establish a general Kronecker limit formula of arbitrary rank over global
function fields with Drinfeld period domains playing the role of upper-half
plane. The Drinfeld-Siegel units come up as equal characteristic modular forms
replacing the classical $\Delta$. This leads to analytic means of deriving a
Colmez-type formula for "stable Taguchi height" of CM Drinfeld modules having
arbitrary rank. A Lerch-Type formula for "totally real" function fields is also
obtained, with the Heegner cycle on the Bruhat-Tits buildings intervene. Also
our limit formula is naturally applied to the special values of both the
Rankin-Selberg $L$-functions and the Godement-Jacquet $L$-functions associated
to automorphic cuspidal representations over global function fields.
