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 In mathematics, the two families ''c''(''x'';''k'') and ''B''(''x'';''k'') of sieved ultraspherical polynomials, introduced by Waleed Al-Salam, W.R. Allaway and Richard Askey in 1984, are the archetypal examples of sieved orthogonal polynomials. The ...
introduced by .
Mourad Ismail
Mourad E. H. Ismail (born April 27, 1944, in Cairo, Egypt) is a mathematician working on orthogonal polynomials and special functions.
Ismail received his bachelor's degree from Cairo University. He holds Masters and doctorate degrees from the U ...
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 In mathematics, sieved Pollaczek polynomials are a family of sieved orthogonal polynomials, introduced by . Their recurrence relations are a modified (or "sieved") version of the recurrence relations for Pollaczek polynomials.
References
*
* ...
, and
sieved Jacobi polynomials In mathematics, sieved Jacobi polynomials are a family of sieved orthogonal polynomials, introduced by . Their recurrence relations are a modified (or "sieved") version of the recurrence relations for Jacobi polynomials.
References
*
*{{Citati ...
.
References
*{{Citation , 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
The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 p ...
, issn=0002-9947 , volume=284 , issue=1 , pages=39–55, jstor=1999273 , citeseerx=10.1.1.308.3668
Orthogonal polynomials