The complementary polynomials and the Rodrigues operator . A distributional study
نویسنده
چکیده
We can write the polynomial solution of the second order linear differential equation of hypergeometric-type φ(x)y + ψ(x)y + λy = 0, where φ and ψ are polynomials, deg φ ≤ 2, degψ = 1 and λ is a constant, among others, by using the Rodrigues operator Rk(φ,u) (see [3]) where u is certain linear operator which satisfies the distributional equation
منابع مشابه
The Complementary Polynomials and the Rodrigues Operator of Classical Orthogonal Polynomials
From the Rodrigues representation of polynomial eigenfunctions of a second order linear hypergeometric-type differential (difference or q-difference) operator, complementary polynomials for classical orthogonal polynomials are constructed using a straightforward method. Thus a generating function in a closed form is obtained. For the complementary polynomials we present a second order linear hy...
متن کاملClassical Orthogonal Polynomials: a General Difference Calculus Approach
It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator with polynomial coefficients. In this paper we present a study of classical orthogonal polynomials in a more general framework by using the differential (or difference) calculus and Operator Theory. In such a way we obtain a unified...
متن کاملM ay 2 00 7 Classical orthogonal polynomials A general difference calculus approach
It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator. In this paper we present a study of classical orthogonal polynomials in a more general context by using the differential (or difference) calculus and Operator Theory. In such a way we obtain a unified representation of them. Furthe...
متن کاملCOMPOSITE INTERPOLATION METHOD AND THE CORRESPONDING DIFFERENTIATION MATRIX
Properties of the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known Legendre interpolation operator. The uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. The appl...
متن کاملAlgebraic adjoint of the polynomials-polynomial matrix multiplication
This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field
متن کامل