Monomial and Rodrigues orthogonal polynomials on the cone
Rabia Aktas, Amilcar Branquinho, Ana Foulquie-Moreno, Yuan Xu

TL;DR
This paper introduces two new families of orthogonal polynomials on a cone in higher-dimensional space, providing explicit constructions and exploring their properties, including biorthogonality and generating functions.
Contribution
It presents explicit constructions of monomial and Rodrigues-type orthogonal polynomials on a cone, expanding the theory of orthogonal polynomials in higher dimensions.
Findings
Explicit formulas for monomial orthogonal polynomials on the cone.
Rodrigues-type formulas for polynomials with Laguerre or Jacobi weights.
Partial biorthogonality between the two polynomial families.
Abstract
We study two families of orthogonal polynomials with respect to the weight function , , on the cone in . The first family consists of monomial polynomials for with , which has the least norm among all polynomials of the form with , and we will provide an explicit construction for . The second family consists of orthogonal polynomials defined by the Rodrigues type formulas when is either the Laguerre weight or the Jacobi weight, which satisfies a generating function in both cases. The two families of polynomials are partially…
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Taxonomy
TopicsMathematical functions and polynomials · Quantum Mechanics and Non-Hermitian Physics · Nonlinear Optical Materials Research
