Clifford algebra-valued orthogonal polynomials in Euclidean space Original Research Article

In this paper a new method for constructing Clifford algebra-valued orthogonal polynomials in Euclidean space is presented. In earlier research, only scalar-valued weight functions were involved. Now the class of weight functions is enlarged with Clifford algebra-valued functions. The method consists in transforming the orthogonality relation on the Euclidean space into an orthogonality relation on the real axis by means of the so-called Clifford–Heaviside functions. Consequently appropriate orthogonal polynomials on the real axis yield Clifford algebra-valued orthogonal polynomials in Euclidean space. Three specific examples of such orthogonal polynomials in Euclidean space are discussed, viz. the generalized Clifford–Hermite, the Clifford–Laguerre and the half-range Clifford–Hermite polynomials.