Observations on power series involving logarithmic singularities

[andydude]

Actually, not quite. For that relationship to be true, technically, then E, F, T etc would have to be Bell matries of those functions. The PDM/Carleman matrix preserves the order of arguments and the Bell matrix reverses it. One way to think about this with two categories. Let (Set) be the category of sets with holomorphic functions as morphisms between them, and let (Vec) be the category of vector spaces with matrices as morphisms between them. Then the Carleman matrix would be a covariant functor and the Bell matrix would be a contravariant functor.

Andrew Robbins