On Linearization Coefficients of Shifted Jacobi Polynomials

This study describes how to represent xmp l(x), p l(x)qm(x) and s. j=1 p l j (x) in terms of shifted Jacobi polynomials (SJPs) using computational methods, where p l (x) and qm(x) are polynomials of degrees l and m, respectively. The suggested problems are discussed when p l (x) and qm(x) are generalized Laguerre, Hermite, and SJPs. In particular, these expansions are presented for the cases of shifted ultraspherical, shifted Legendre, and shifted Chebyshev polynomials of the first and second kinds.