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Two families of associated Wilson polynomials. (English) Zbl 0712.33005
The Wilson polynomials are the most general classical type orthogonal polynomial which can be written as a hypergeometric series. They satisfy a three term recurrence relation whose coefficients are rational functions of n. Shift the variable in these rational function by a real parameter. Using work of Bailey, Orr and Whipple from the end of the last century through the next 40 years, the authors find an explicit representation for these polynomials and the continuous component of the orthogonality measure. There is a second type of associated polynomials, when the recurrence coefficients are the same, but the initial conditions are slightly modified. The second class of polynomials is also treated. The usual continued fraction is computed. The continued fractions can contain very interesting special cases.
Reviewer: R.Askey
33C45Orthogonal polynomials and functions of hypergeometric type
42C05General theory of orthogonal functions and polynomials