If Sigma(infinity)(k=0) c(k)g(k)(x) is a formal series of orthonormal polynomials g(k) (x) on the real line with positive oefficients ck, then its partial sums u(n)(x) are associated with Jacobi-type pencils. Therefore, they possess a recurrence relation and special orthonormality conditions. The cases where g(k)(x) are Jacobi or Laguerre polynomials are of especial interest. For a suitable selection of parameters c(k), the partial sums u(n)(x) turn into Sobolev orthogonal polynomials with a (3 x 3) matrix measure. Moreover, by the subsequent choice of parameters, we get differential equations for u(n). In the last case, the polynomials u(n), (x) are solutions of generalized eigenvalue problems both in x and in n.
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