A Brief Account on Special Trilinear Functions and their Applications

Based on previous works on special bilinear functions (SBF), we present their use in evaluating Chebyshev polynomials showing the beauty of the SBF technique. Then, as a generalisation of SBF, we define special trilinear functions (STF) of three n-tuples vectors. Finally, a few applications are given, such as taking the product of three polynomials of degree n, emphasising the fact that the process of computing the product of three integers using STF methods occurs in a very efficient manner and with no stated effort. A short discussion on the future of the subject constitutes the conclusion of our study.