Monomiality, orthogonal and pseudo-orthogonal polynomials

Monomiality, Orthogonal and Pseudo-orthogonal Polynomials

We reconsider some families of orthogonal polynomials, within the framework of the so called monomiality principle. We show that the associated operational formalism allows the framing of the polynomial orthogonality using an algebraic point of view. Within such a framework, we introduce families of pseudo-orthogonal polynomials, namely polynomials, not orthogonal under the ordinary definition,...

Associated Laguerre Polynomials: Monomiality and Bi–Orthogonal Functions

We exploit the concepts and the formalism associated with the principle of monomiality to derive the ortogonality properties of the associated Laguerre polynomials. We extend a recently developed technique of algebraic nature and comment on the usefulness of the proposed method.

Orthogonal Polynomials with Orthogonal Derivatives

Symmetric Orthogonal Polynomials and the Associated Orthogonal L-polynomials

We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained. Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx2)(l x2)~1/2, k>0.

Orthogonal Polynomials

The theory of orthogonal polynomials plays an important role in many branches of mathematics, such as approximation theory (best approximation, interpolation, quadrature), special functions, continued fractions, differential and integral equations. The notion of orthogonality originated from the theory of continued fractions, but later became an independent (and possibly more important) discipl...