Matrices of the Differential D/DX and X(D/DX) with Respect to Orthonormal Bases of Jacobi Polynomials

摘要

The normalized eigenvectors which are the normalized Jacobi's polynomials R, of the second order linear differential Jacobi's operator, positive and self-adjoint, acting over Hilbert Space X of square integrable functions, are considered. The differential operator D (derivative with respect to X) and L (x times D) acting over R, are discussed. Matrix entries of inner product of the action of L and D over R by the normalized eigenvectors R, are calculated.