## Sieved ultraspherical polynomials

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- by Waleed Al-Salam, W. R. Allaway and Richard Askey PDF
- Trans. Amer. Math. Soc.
**284**(1984), 39-55 Request permission

## Abstract:

The continuous $q$-ultraspherical polynomials contain a number of important examples as limiting or special cases. One of these arose in Allaway’s Ph.D. thesis. In a previous paper we solved a characterization problem essentially equivalent to Allaway’s and showed that these polynomials arose from the $q$-ultraspherical polynomials when $q$ approached a root of unity. A second class of such polynomials is found, and the recurrence relation and orthogonality relation are found for each of these polynomials. The orthogonality is interesting because the weight function has a finite number of zeros in $(-1, 1)$. Generating functions and other formulas are also found.## References

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## Additional Information

- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**284**(1984), 39-55 - MSC: Primary 33A45; Secondary 33A65, 42C05
- DOI: https://doi.org/10.1090/S0002-9947-1984-0742411-6
- MathSciNet review: 742411