A combinatorial determinant

Herbert S. Wilf

Published 1998-09-22, updated 1998-10-25Version 3

A theorem of Mina evaluates the determinant of a matrix with entries $D^j(f(x)^i)$. We note the important special case where the matrix entries are evaluated at $x=0$ and give a simple proof of it, and some applications. We then give a short proof of the general case.