The Classical Orthogonal Polynomials

To prove (7.07), for example, let &,(x) denote the right-hand side and w(x) be any polynomial. Then by repeated partial integrations we arrive at

I ( l - x ~ ( l + ~ ) ~ ~ ~ ( x ) m ( x ) d x = ( 1 -x)"+"(l + ~ ) " + ~ m ' " ' ( x ) dx.