Abstract
An approach to general bivariate Appell polynomials based on matrix calculus is proposed. Known and new basic results are given, such as recurrence relations, determinant forms, differential equations and other properties. Some applications to linear functional and linear interpolation are sketched. New and known examples of bivariate Appell polynomial sequences are given.
Highlights
Appell introduced a class of polynomials by the following equivalent conditions: { An }n∈IN is an Appell sequence (An being a polynomial of degree n) if either
To the best of authors knowledge, a systematic approach to general bivariate Appell sequences does not appear in the literature
The previous recurrence relations provide determinant forms [36,37], which can be useful for both numerical calculations and new combinatorial identities
Summary
To the best of authors knowledge, a systematic approach to general bivariate Appell sequences does not appear in the literature. The paper is organized as follows: in Section 2 we give the definition and the first characterizations of general bivariate Appell polynomial sequences; in Sections 3–5 we derive, respectively, matrix form, recurrence relations and determinant forms for the elements of a general bivariate Appell polynomial sequence. These sequences satisfy some interesting differential equations (Section 6) and properties (Section 7).
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