Clifford–Hermite Polynomials in Fractional Clifford Analysis

Abstract

Abstract. In this paper we generalize and standardize Clifford-Hermite polynomials to the new framework of fractional Clifford analysis with respect to the Riemann-Liouville derivative in a symbolic way. As the main consequence of this approach, one does not require an a priori integration theory. Basic properties such as orthogonality relations, differential equations, and recursion formulas, are proven. Mathematics Subject Classification (2010). Primary 30G35; Secondary 26A33; 42C05; 30H99.