Wilson polynomials and some continued fractions of Ramanujan (Q810217)

The Wilson polynomials are a set of balanced \({}_ 4F_ 3's\) which are orthogonal, and so satisfy a three term recurrence relation. These polynomials depend on four free parameters. When the sum of these parameters is 1 or 2 there is a second polynomial solution to these recurrence relations which arises from a different way of treating an indeterminate form. In these two cases, the new orthogonality relation is found. In each case, a continued fraction found by Ramanujan is shown to occur, and natural evaluations of those continued fractions are given. An outline of a q-extension is given.