Explicit calculation of some polynomials introduced by W. Gautschi

Introduction The polynomials in question were introduced by W. Gautschi when he analyzed the numerical condition of the method of modified moments: Let oe be a given positive measure with infinite support S(oe). Then there uniquely exists a family of monic polynomials ß j with Z ß l (x)ß j (x) doe(x) = 0 for l ! j and Z ß 2 j (x) doe(x) ? 0; j = 0; 1; : : : They satisfy a three-term recurrence relation ß j+1 (x) = (x \Gamma ff j )ß j (x) \Gamma fi j ß j<F2