Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424959 | Advances in Mathematics | 2016 | 28 Pages |
Abstract
We present an algebraic theory of orthogonal polynomials in several variables that includes classical orthogonal polynomials as a special case. Our bottom line is a straightforward connection between apolarity of binary forms and the inner product provided by a linear functional defined on a polynomial ring. Explicit determinantal formulae and multivariable extension of the Heine integral formula are stated. Moreover, a general family of covariants that includes transvectants is introduced. Such covariants turn out to be the average value of classical basis of symmetric polynomials over a set of roots of suitable orthogonal polynomials.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
P. Petrullo, D. Senato, R. Simone,