Weak classical orthogonal polynomials in two variables
Copyright policy )Weak classical orthogonal polynomials in two variables
The paper contains 6 definitions, 3 lemmas, 4 propositions and 2 corollaries. The authors first introduce the concept of weak classical orthogonal polynomials in two variables. Next, three characterizations for weak classical orthogonal polynomials are established: the orthogonality of the gradients; the structure relation; and the matrix Bochner-type second-order partial differential equation. Then, some consequences of the characterizations are given. At the end, as a special case, the Krall and Sheffer classical orthogonal polynomials in two variables are recorded.
- University of Granada Spain
- University of Granada (UGR) Spain
Computational Mathematics, Applications of hypergeometric functions, Applied Mathematics, Classical orthogonal polynomials, Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable, weak classical orthogonal polynomials, moment functional, Connections of hypergeometric functions with groups and algebras, and related topics, Other special orthogonal polynomials and functions, Orthogonal polynomials in two variables, Pearson differential equation
Computational Mathematics, Applications of hypergeometric functions, Applied Mathematics, Classical orthogonal polynomials, Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable, weak classical orthogonal polynomials, moment functional, Connections of hypergeometric functions with groups and algebras, and related topics, Other special orthogonal polynomials and functions, Orthogonal polynomials in two variables, Pearson differential equation
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