Algebraic formulas and Geometric derivation of Source Identities

TL;DR

This paper provides a geometric derivation of source identities involving multivariable special functions, extending determinant representations to elliptic versions and presenting symmetrization formulas.

Contribution

It introduces a systematic geometric approach to derive and extend source identities, including elliptic determinant formulas and symmetrization techniques.

Findings

Derived geometric proofs for rational and trigonometric source identities

Extended determinant representations to elliptic functions

Presented symmetrization formulas for rational source functions

Abstract

Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant representations for source functions which appeared in previous literature as well as introducing the elliptic version of the determinants, and obtain identities between determinants. We also show several symmetrization formulas for the rational version.