Symbolic approach to the general quadratic polynomial decomposition
\^Angela Macedo, Teresa Mesquita, Z\'elia da Rocha
TL;DR
This paper introduces a symbolic method for decomposing general quadratic polynomials, exploring properties like orthogonality and symmetry, and providing explicit results for well-known orthogonal cases.
Contribution
It presents a novel symbolic approach to quadratic polynomial decomposition, analyzing properties and offering explicit results for specific orthogonal cases.
Findings
Identified conditions for orthogonality in polynomial components
Demonstrated symmetry properties in the decomposition
Provided explicit formulas for classical orthogonal polynomials
Abstract
In this work we deal with a symbolic approach to the general quadratic polynomial decomposition. By means of a symbolic implementation, we investigate some properties of the components sequences like orthogonality and symmetry. We present some explicit results for a collection of well known orthogonal cases.
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