Cauchy type identities and corresponding fermatian matrices via non-comuting variables of extended finite operator calculus

TL;DR

This paper introduces a new family of extended Cauchy identities and related Fermat matrices using non-commuting variables from extended finite operator calculus, expanding potential applications.

Contribution

It develops novel extended Cauchy identities and Fermat matrices based on non-commuting variables within extended finite operator calculus, a framework previously introduced by the author.

Findings

New extended Cauchy type identities discovered

Fermat type matrices constructed for extended applications

Framework ready for broader mathematical applications

Abstract

New family of extended Cauchy type identities is found and related Fermat type matrices are provided ready for applications in extended scope. This is achieved due to the use specifically non-commuting variables of extended finite operator calculus introduced by the author few years ago.