The rotational invariants constructed by the products of three spherical harmonic polynomials

TL;DR

This paper develops a general method to explicitly express rotational invariants formed by products of three spherical harmonic polynomials as homogeneous polynomials, with calculated coefficients.

Contribution

It provides explicit formulas for the coefficients of rotational invariants constructed from three spherical harmonic polynomials.

Findings

Explicit expressions for the coefficients of the invariants.

General homogeneous polynomial representation of the invariants.

Enhanced understanding of rotational invariants in harmonic analysis.

Abstract

The rotational invariants constructed by the products of three spherical harmonic polynomials are expressed generally as homogeneous polynomials with respect to the three coordinate vectors, where the coefficients are calculated explicitly in this paper.