sieved orthogonal polynomials

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In mathematics, sieved orthogonal polynomials are orthogonal polynomials whose recurrence relations are formed by sieving the recurrence relations of another family; in other words, some of the recurrence relations are replaced by simpler ones. The first examples were the sieved ultraspherical polynomials introduced by {{harvs|txt | last1=Al-Salam | first1=Waleed | last2=Allaway | first2=W. R. | last3=Askey | first3=Richard | title=Sieved ultraspherical polynomials | doi=10.2307/1999273 | mr=742411 | year=1984 | journal=Transactions of the American Mathematical Society | issn=0002-9947 | volume=284 | issue=1 | pages=39–55}}. Mourad Ismail later studied sieved orthogonal polynomials in a long series of papers. Other families of sieved orthogonal polynomials that have been studied include sieved Pollaczek polynomials, and sieved Jacobi polynomials.