Orthogonal polynomials with orthogonal derivatives

  title={Orthogonal polynomials with orthogonal derivatives},
  author={Michael S Webster},
p(x)xdx, Pi = I q(x)xdx, i = 0, 1, • • • , a J a p(x) ^ 0, q(x) ^ 0, a0> 0, j80 > 0. Lebesgue integrals are used and the interval {a, b)\ may be finite or infinite. We are concerned with the following assertion: THEOREM. If {<f>n(x)} and {<t>n (x)} are orthogonal systems of polynomials, then {<l>n(x)} may be reduced to the classical polynomials of Jacobi, Laguerre, or Hermite by means of a linear transformation on x.