The parabolic mean operator and related polynomial sequence: a theoretical approach

In this article, a new operator is introduced, called parabolic mean operator. The related polynomial sequences are determined. They are new Appell sequences. These sequences are studied mainly from a theoretical point of view, favoring a matrix approach. Explicit monomial expression, matrix form, recurrence relations and determinat forms for the polynomials of the sequences are given. The linear functional associated with the first determinant form, which generates the orthogonal conditions and the representation of the polynomials, is considered. Finally, the bidimensional case closes the paper.