Formal power series and loose entry formulas for the Dixon matrix

Abstract

Formal power series are used to derive four entry formulas for the Dixon matrix. These entry formulas have uniform and simple summation bounds for the entire Dixon matrix. When corner cutting is applied to the monomial support, each of the four loose entry formulas simplifies greatly for some rows and columns associated with a particular corner, but still maintains the uniform and simple summation bounds. Uniform summation bounds make the entry formulas loose because redundant brackets that eventually vanish are produced. On the other hand, uniform summation bounds reveal valuable information about the properties of the Dixon matrix for a corner-cut monomial support. © Springer-Verlag Berlin Heidelberg 2005.