Special bilinear functions (SBF) proved to be applicable in many situations and for a good number of problems. Hence it is important to generalize them to a higher degree by expanding previous work. In the beginning, ...Special bilinear functions (SBF) proved to be applicable in many situations and for a good number of problems. Hence it is important to generalize them to a higher degree by expanding previous work. In the beginning, we give a quick review of SBF [or quacroms of second degree and dimension 2 x <em>n</em>];then we give a few applications based on previously published research concentrating on their use in evaluating some special functions and where we present the evaluation of Chebyshev polynomials as a new work. Following that, we define special trilinear functions (STF) of three <em>n</em>-tuples vectors, which are the generalization of SBF. Finally, a few applications, such as taking the product of three polynomials of degree <em>n</em>, are given stressing the fact that the process of taking the product of three integers using STF techniques, practically, takes place in a very efficient way and with no mentioned effort. A short discussion on the future of the subject constitutes the conclusion of our article.展开更多
文摘Special bilinear functions (SBF) proved to be applicable in many situations and for a good number of problems. Hence it is important to generalize them to a higher degree by expanding previous work. In the beginning, we give a quick review of SBF [or quacroms of second degree and dimension 2 x <em>n</em>];then we give a few applications based on previously published research concentrating on their use in evaluating some special functions and where we present the evaluation of Chebyshev polynomials as a new work. Following that, we define special trilinear functions (STF) of three <em>n</em>-tuples vectors, which are the generalization of SBF. Finally, a few applications, such as taking the product of three polynomials of degree <em>n</em>, are given stressing the fact that the process of taking the product of three integers using STF techniques, practically, takes place in a very efficient way and with no mentioned effort. A short discussion on the future of the subject constitutes the conclusion of our article.
