The algebraic recursive determination of matrix elements of some selected families of functions Q1(x) between the solutions Psi jm(x) of factorisable equations is reinvestigated. The possibilities of the procedure outlined in a previous paper are enlarged by using the connection between factorisation types, i.e. the different possible factorisations of the same differential equation. The computation of matrix elements between the Jacobi eigenfunctions Psi jm(x) approximately=(sin(ax/2))alpha +1/2 (cos(ax/2))beta +12/Pv( alpha , beta )(cos ax), where a is a real or pure imaginary constant, is studied in detail. Algebraic recurrence formulae satisfied by matrix elements of Qt(x)=(cos(ax/2))p(sin(ax/2))q(tan(ax/2))t, Qt(x)=(sin(ax))p(tan(ax))q(cos(ax))t, Qt(x)= Psi jt(x) and Qt(x)= Psi tm(x) are given, and, for the particular cases Qt(x)=(tan(ax/2))t and Qt(x)=(cos ax)t, closed-form expressions are obtained. As an illustrative application, it is briefly shown how the expressions can serve to derive analytical approximations of the bound-state energies for the potential V(x)=A exp(-x2)-l(l+1)/x2. Some further applications are pointed out.