2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58957In this paper we compare several properties and constructions of the Carlitz polynomials and digit derivatives for continuous functions on $\F_q[[T]].$ In particular, we show a close relation between them as orthonormal bases. Moreover, parallel to Carlitz's coefficient formula, we give the closed formula for the expansion coefficients in terms of the digit derivatives.Number Theorytext