In number theory, explicit formulas for the special values of L-functions and p-adic L-functions are of great interest. For instance, the classical Leopoldt's formula expresses the value of the Kubota-Leopoldt p-adic L-function at s=1 in terms of logarithm of algebraic numbers called cyclotomic units. In this thesis, we extend this result to characteristic p v-adic L-functions for certain function fields, where v is a "finite place" of the function field. This extends the work of Anderson, who first showed a formula for L-functions and v-adic L-functions for F_q[t], as well as of Lutes, who extended Anderson's result for L-functions for any function field. Our result is achieved by factoring the coefficients of logarithm series in function fields, and hence showing the v-adic convergence of such series. Speaker(s): Angus Chung (UM)