Computing expansions coefficients for Laguerre polynomials

This paper reports computational manipulation to express xmpn(x), pn(x)qm(x) and ∏j=1spnj(x) in terms of generalized Laguerre polynomials, where pn(x) and qm(x) are polynomials of degrees n, m, respectively. The presented analytical formulae are discussed when pn(x) and qm(x) are generalized Laguerre, Hermite and Jacobi polynomials. Also, the corresponding formulae for the cases of Legender polynomials and Chebysheve polynomials of first, second, third and fourth kinds, are discussed.