A Comparison of the Carlitz and Digit Derivatives Bases in Function Field Arithmetic, by Sangtae Jeong
In 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.